As stated, you can't update the flash player. There is no PPC version of it. There are workarounds to make flash work (only for youtube I think, though) using M-player but the quality is bad and just isn't worth doing. I have it setup to do so but it's a waste.
However, you can setup a Media Server on your PC and use it on the PS3's XMB. You can use Windows Media Player 11 (I use this 1 and works great), VLC Media Player, TVersity, and others.
PS3 Model - 80 GB/Non PS2-BC
PS3 Version - CECHL01
Modification(s) - Official Firmware 4.00
Purchased - March 27th, 2009
PS2 Model - Slimline/SCPH-77001
PS2 Version - V15
Modification(s) - UlaunchElf 4.42/Free MC Boot 1.8b
Purchased - April 16, 2007