Not used it, and it looks as if it only works with Firefox, but GNASH
http://www.gnu.org/software/gnash/ is a free Flash alternative. Apparently it doesn't play too well with newer Flash files, so you may not get much use out of it.
If you haven't already tried this, there's a list of ways to try to get Flash Player running here:
http://www.adobe.com/go/tn_19166
If it's just a question of playing downloaded Flash files, Real Player (yuck), GOM Player, VLC and The KMPlayer (my favourite, mainly on aesthetics) all play .flv files.