I honestly don't know if Brian Flores has evidence of discrimination or that he was only being interviewed out of compliance with the Rooney Rule with no real chance of getting a head coaching job of which I'm unaware. I am confident in saying that the Dolphins probably made a bad move by firing him and that it does surprise me that he didn't get a new head coaching job. Still, none of that is evidence.
One thing that I'm compelled to point out is the fact that Flores is a defensive minded coach and that only two of the eight teams that hired a new head coach opted for an offensively minded coach. Three out the four teams being sued by Flores went with a former offensive coordinator and desperately need somebody who can develop a quarterback and, it's safe to say that Tua is still underdeveloped after a couple of years with Flores. The Texans were added to the lawsuit later and they did hire a defensive minded head coach. The issue there is that they also hired a black head coach and Lovie Smith has a much more impressive resume than Flores - Smith coached a team to the Super Bowl and Flores has yet to make the playoffs.
It seems to me that Flores's best shot is to prove that the Texans refused to hire him out of retaliation for him blowing a whistle against the NFL. Lovie Smith wasn't even announced as a finalist for the Texans job and was suddenly hired seemingly out of the blue. He might have a legitimate case against the Dolphins if there's any proof that he was pressured to lose games.
Still, I don't see much of a case here in general. Maybe some of the teams will just try to settle. I've gotta imagine that the Broncos, Giants, and Dolphins particularly will want to save face though. Those three teams also have clear reasons why they would go for a coach other than Flores.