i would vote for vlc, but you should check out media monkey for audio...it's also compatible with ipods if you don't like itunes. try converting the flash video files with any video converter or something similar to see if it plays more stable
Why do you need one player that plays them all? I use Media Player for most avi/wmv/mpg; VLC for long videos because I can fastforward/slomo; Realplayer which i rarely see now; Quicktime and Adobe for Flash...but that's on Windows. On Linux I use Gnomeplayer or VLC for everything.