Can you separate the Flash player from Chrome and make P-Firefox use it?

Can you separate the Flash player from Chrome and make P-Firefox use it? I'm using P.A. on a school computer with some odd Deep Freeze app that resets the computers, except for a network drive, every reboot for ultimate virus protection, meaning that flash is always out of date, as well as everything else. Is it possible to copy the built-in flash player from Chrome and put it in a standalone thing? Or maybe set it up so Firefox can run it? I guess I could just keep using firefox but it has all my password cookies!