I agree the built in browser supports flash while firefox really sucks on android.
If you must have an alternative to the built in browser, try opera mini. No flash either.
Or for flash, try skyfire. It doesn't really support flash, it runs everything through their own proxy servers which processes the flash videos and relays it to your installed skyfire browser.
I think the built-in browser actually runs flash because I don't see it going through a proxy or some server side pre processor.