Adobe no longer supports Flash on Linux; the latest version of Flash available for Linux is 11.2 (while everybody else is on version 13 or 14).
Have you tried Google Chrome? I go back and forth between Firefox and Chrome, but Chrome does have its own built-in Flash player. It would be interesting to see if you have more success with it. About the only thing I use Flash for on Linux, however, is watching a YouTube video, and both browsers seem to run it fine...though I'm using Xubuntu and not Mint.