Having grappled with this problem myself for the last few weeks, I did some research into it. My impressions are these:
- Google purchased Flash from Adobe and have incorporated it into the Google Chrome web browser using a different API than that used by Firefox (PPAPI vs. NPAPI),
- If you want proper Flash support under 64 bit Linux right now, your only choice is to use Google Chrome,
- The general consensus among developers seems to be that Flash will be dead within 5 years, so why bother with it?