Flores alleged in the suit that the NFL is rife with racism and has a "disingenuous commitment to social equity".
He is suing the league along with teams at whose hands he claims he experienced racism, naming former team the Miami Dolphins along with the Giants and Denver Broncos as defendants, together with "John Doe Teams 1 through 29".
The NFL said Flores' claims "are without merit", saying it would put up a defence. The three teams named by Flores also rejected his allegations.
Among the allegations made by Flores is that he inadvertently learned he had failed to get the Giants job last week before his interview, which the lawsuit claims was "a sham" that "humiliated" him.
The suit contains screen grabs of an alleged text message conversation between New England Patriots coach Bill Belichick and Flores, in which Belichick congratulates Flores on what he believes is an impending appointment, only to realise he was messaging the wrong person, having intended to contact Brian Daboll, who got the Giants job.
During the text exchange, Flores questioned whether Belichick had messaged the correct person, with the Patriots coach having indicated he had inside knowledge on who would land the job.
According to the lawsuit's contents, Belichick at this point realised his error and apologised to Flores, who worked for him for 10 years with the Patriots.
However, the Giants released a lengthy statement on Thursday, saying: "The decision on who we would hire as head coach was made on the evening of January 28, one day after Mr. Flores spent an entire day in our offices going through his second interview for the position, meeting with ownership and other staff members, and receiving a tour of our facility."
The team added Belichick would have no knowledge of any decision, as the alleged conversation suggested.
"The allegation that the Giants' decision had been made prior to Friday evening, January 28, is false," the Giants said.
"And to base that allegation on a text exchange with Bill Belichick in which he ultimately states that he 'thinks' Brian Daboll would get the job is irresponsible.
"The text exchange occurred the day before Coach Daboll's in-person interview even took place. Giants' ownership would never hire a head coach based only on a 20-minute zoom interview, which is all that Mr. Daboll had at that point.
"In addition, Mr. Belichick does not speak for and has no affiliation with the Giants. Mr. Belichick's text exchange provides no insight into what actually transpired during our head coaching search."
The Giants included a timeline of Flores' day at their facility and said: "We hired Brian Daboll as our head coach at the conclusion of an open and thorough interview process. No decision was made, and no job offer was extended, until the evening of January 28, a full day after Mr. Flores' in-person interview and day-long visit to the Giants."
Flores, who led the Dolphins for three seasons before being controversially fired following the 2021 campaign, spent this past season as a senior defensive assistant and linebackers coach for the Pittsburgh Steelers.
The 41-year-old filed a class-action lawsuit against the NFL alleging racial discrimination in its hiring practices following his dismissal from Miami.
The Dolphins were also included in the complaint, which is still pending, as well as two other teams, the Denver Broncos and New York Giants.
Flores, who is black, alleged he spoke with the Broncos and Giants for open head coaching positions only to satisfy the NFL's Rooney Rule that requires teams to interview minority candidates for such vacancies.
Prior to taking over in Miami, Flores spent 11 seasons on Bill Belichick's staff with the New England Patriots, including the last three as linebackers coach.
He handled defensive play-calling duties in his final season with New England in 2018, helping the Pats to a 13-3 win over the Los Angeles Rams in Super Bowl LIII.
Flores compiled a 24-25 record with the Dolphins, with winning seasons in both 2020 and 2021, though Miami missed out on the playoffs both years.
The Browns fired defensive coordinator Joe Woods shortly after their season ended with Sunday's 28-14 loss to the Steelers.
Cleveland previously interviewed ex-Detroit Lions head coach Jim Schwartz, a former DC for the Tennessee Titans, Buffalo Bills and Philadelphia Eagles, for the opening on Wednesday.
Last month, the Dolphins handed Tagovailoa a franchise-record four-year, $212.4million extension off the back of an impressive fourth season with the team.
Tagovailoa posted career-best figures for passes attempted (560), completed (388), passing yards (4,624) and touchdown passes (29) in 2023, though Miami fell at the first hurdle in the playoffs, losing 26-7 to the eventual Super Bowl LVIII champions, the Kansas City Chiefs.
Tagovailoa has improved season-on-season since being drafted fifth overall by Miami in 2020, with his two best campaigns coming since McDaniel replaced Flores as head coach in 2021.
The quarterback has now hit out at the way Flores – who is entering his second year as defensive coordinator with the Minnesota Vikings – drained his confidence.
He said in an interview with The Dan LeBatard Show: "To put it in the simplest terms, if you woke up every morning and I told you that you suck at what you did, that you don't belong, that you shouldn't be here, that you haven't earned this right...
"Then you have somebody else come in and tell you, 'dude, you are the best fit for this'... How would it make you feel, listening to one or the other?
"You hear it, no matter what it is, the good or the bad, you hear it more and more, you start to believe that. I don't care who you are.
"You could be the president of the United States, you have a terrible person telling you things that you don't want to hear or probably shouldn't be hearing, you're going to start believing that about yourself.
"That's what ended up happening. It was basically two years of training that out of not just me but a couple of other guys as well."
The Dolphins open their 2024 campaign at home to the Jacksonville Jaguars on September 8 before facing the Buffalo Bills, their AFC East rivals, four days later.
Flores, who is now the Minnesota Vikings defensive coordinator, expressed his regret about how he handled their relationship when he was the head coach of the Dolphins.
In an interview with The Dan LeBatard Show on Monday, Tagovailoa described Flores as a "terrible person" during the time they spent together between 2019 and 2022.
Tagovailoa posted career-best figures for passes attempted (560), completed (388), passing yards (4,624) and touchdown passes (29) in 2023 and was handed a franchise-record four-year, $212.4million extension off the back of an impressive fourth season with the team.
On Tuesday, Flores addressed the situation during a session with reporters, saying: "I'm genuinely, genuinely happy for the success that Tua has had and I really wish him nothing but the best.
Flores said he's done a lot of reflecting since hearing the comments and admitted he had some faults in Miami, although he did not say anything said by Tagovailoa was untrue.
"I think part of coaching is correcting," Flores said. "I'm always going to correct. I'm always going to have a high standard.
"And I think, look, I've done a lot of reflecting on the situation, reflecting on the situation and communication."
"I think there's things that I could do better for sure, and I've grown in that way, and I've tried to apply the things that I could do better and the things that I've learned over the last two, three years.
"But I would say over the long haul, I've had a lot of great relationships over my 21-year career here in the league. Players, coaches, personnel, equipment, people in the kitchen.
"I mean really across the board, I've had a lot of great relationships. I'm going to continue to do that, but I'm also always looking to get better and involved."
Flores has launched a class action lawsuit, alleging the NFL is rife with racism and has a "disingenuous commitment to social equity".
In the suit, Flores alleges that when he interviewed for the role of head coach with the Broncos in 2019, Elway and former Denver executive Joe Ellis were late and appeared "completely dishevelled" from an evening of heavy drinking.
Flores is suing the league along with teams from which he alleges he has personally experienced racism, naming the Dolphins and the Broncos along with the New York Giants as defendants, together with "John Doe Teams 1 through 29".
The suit, filed at the United States District Court for the Southern District of New York, demands a jury trial. The NFL said Flores' claims "are without merit", adding that it would put up a defence. The three teams named by Flores have also rejected his allegations.
The NFL has a 'Rooney Rule' in place that requires all teams seeking a new head coach "to interview at least one or more diverse candidates".
It is alleged in the lawsuit that Flores "was interviewed only because of the Rooney Rule" by the Broncos and was never intended to be "a legitimate candidate", while also criticising the interview board.
The Broncos described the various claims against the franchise as "blatantly false" and "baseless and disparaging", to which Flores responded on ESPN's Get Up! show on Wednesday, saying: "I deal in truth, that's my reaction. I deal in truth. Honesty, integrity is important to me, and hopefully, there's a day we find out the truth on that one."
Elway released a statement on Thursday to further deny the claims made by Flores, saying: "While I was not planning to respond publicly to the false and defamatory claims by Brian Flores, I could not be silent any longer with my character, integrity and professionalism being attacked.
"I took Coach Flores very seriously as a candidate for our head coaching position in 2019 and enjoyed our three-and-a-half-hour interview with him. Along with the rest of our group, I was prepared, ready and fully engaged during the entire interview as Brian shared his experience and vision for our team.
"It's unfortunate and shocking to learn for the first time this week that Brian felt differently about our interview with him.
"For Brian to make an assumption about my appearance and state of mind early that morning was subjective, hurtful and just plain wrong. If I appeared 'dishevelled,' as he claimed, it was because we had flown in during the middle of the night - immediately following another interview in Denver - and were going on a few hours of sleep to meet the only window provided to us.
"I interviewed Brian in good faith, giving him the same consideration and opportunity as every other candidate for our head coaching position in 2019."
The Broncos recently appointed Green Bay Packers offensive coordinator Nathaniel Hackett as their new head coach, having parted company with previous head coach Vic Fangio, who was hired in 2019.
Fangio achieved a 19-30 record during his three seasons with the franchise, failing to reach the playoffs throughout his tenure.
Flores was fired from his role as head coach of the Miami Dolphins in January following the franchise's first back-to-back winning seasons since 2003, finishing 10-6 in 2020 and 9-8 in 2021.
During the fallout of his stint in Miami, Flores filed a lawsuit against the NFL, the Dolphins, Denver Broncos and New York Giants.
In it, he accused the Broncos and Giants of flawed hiring processes, alleging the two franchises only offered interviews to comply with the league's 'Rooney Rule', which requires teams to interview candidates of colour for head coaching and senior operation vacancies.
The class action brought by Flores alleged the NFL "remains rife with racism, particularly when it comes to the hiring and retention of black head coaches, coordinators and general managers".
Flores also alleged he was offered $100,000 per loss by Dolphins owner Stephen Ross in 2019 in an effort to secure a better draft position.
All parties have strenuously denied Flores' allegations.
Flores was confirmed as the Steelers' new defensive assistant and linebackers coach last month, and Tomlin acknowledged that his decision to offer him a role was partly influenced by a desire to ensure he was not exiled from the league.
"I just didn't want him to feel like he was on an island," he told reporters on Sunday.
"From a coaching fraternity standpoint, I owed him that. I was in position to provide that. I think that started our interactions and conversations.
"Over the course of those discussions, particularly when it became evident he was not going to get a head job, then I think the natural discussion began.
"It really ran its course rather quickly, to be quite honest with you, because it doesn't require a lot of time to come to the realisation that you can use a Brian Flores on your staff."
Tomlin believes Flores will bring a level of experience that will help shape decision-making on every level.
"Senior defensive assistant and linebacker coach is his title, but there's help that he's going to help us and help me, in particular," he added.
"I love sharpening my sword on his and gaining a perspective that his experiences provide, that wise counsel.
"We're talking about a myriad of things. Whether it's calendar, whether it's taking care of players, whether it's the acquisition or evaluation of talent, it's been fun to have him. His contributions are going to be significant."
Flores, who went 24-25 in three seasons with the Dolphins before being controversially fired following the 2021 campaign, spent this past season as a senior defensive assistant and linebackers coach for the Pittsburgh Steelers.
The 41-year-old previously served 11 seasons on Bill Belichick’s staff with the New England Patriots before joining Miami in 2019. Flores was part of four Super Bowl-winning teams with New England and handled defensive play-calling duties in his final season there in 2018, helping the Pats to a 13-3 win over the Los Angeles Rams in Super Bowl 53.
ESPN reported Sunday that Flores was one of three finalists, along with New York Giants offensive coordinator Mike Kafka and Cincinnati Bengals defensive coordinator Lou Anarumo, for the Arizona Cardinals head coaching position that remains unfilled. He also previously spoke with the Cleveland Browns and Atlanta Falcons for those teams' defensive coordinator openings.
Flores replaces Ed Donatell, who was fired shortly after Minnesota's 31-24 loss to the Giants in the opening round of the playoffs. The Vikings finished this past season 31st among the NFL's 32 teams in both total yards allowed and passing yards allowed and were tied for 28th in scoring defence after yielding 25.1 points per game.
In his lone season with the Steelers, Flores was part of a staff that helped the Steelers allow just seven rushing touchdowns – tied for the fewest in the NFL – and had the league’s sixth-lowest completion percentage against (61.3 per cent).
Flores, who is Black, still has a class-action lawsuit pending against the NFL alleging racial discrimination in its hiring practices following his dismissal by the Dolphins in January 2022.
The suit also alleged that the Giants and Denver Broncos interviewed Flores for open head coaching positions only to satisfy the league’s Rooney Rule that requires teams to interview minority candidates for such vacancies.
