Is there something that blocks you from logging in on Firefox if you have logged in on Chrome? I type in my username and password and it doesn't log me in when I use Firefox, and I can't play Unity games on Chrome anymore. I can't even create a new account using Firefox, is there anything I can do to log in on Firefox?
I've just tried it, it seems to work fine. Maybe you should try offline mode on Firefox. See if that helps. Otherwise trying clearing cache, but that may delete some of your local save files from flash games.