Its not only believable, it happens all the time (just on a smaller scale).
As for Flores' individual motivation, I don't know the guy. Perhaps he's unable to accept his own shortcomings, and has been persuaded to take this fight on by others. Perhaps he sees it as his calling, even more so than coaching.
You seem to have concluded that a worthy "principle" is involved. I'm not so sure. While I'm sure there are individual hiring/firing decisions in the NFL that are tainted with discriminatory motives, alleging that its a systemic issue within the NFL (which would essentially require proof of collusion or collective action) is pretty far-fetched. That's not to say that one can't try to make that case, but when I see absurd allegations in a Complaint describing the NFL as being like a "plantation" merely because the owners are almost exclusively white and the players are 70% black, I stop taking the matter seriously.