It's been a while since I've worked with Flash, but IIRC you wouldn't want to convert to flash, but would want to embed a movie in a flash animation. Why do you want it flash anyway, if it's just going to be the video? The only reason that I know of to use flash is to take advantage of its capabilities.
98% of people also already have quicktime installed, and many people turn off their flash plugin, since flash animations are often intrusive and obnoxious.
Anyway, in regards to the original question, I don't know, maybe somebody else can help you. 🙂
2 things:
1 - if you have Flash Pro you can convert mpeg, etc to FLV files (flash video). You can also buy Sorenson Squeeze ($99) to do the same thing.
2 - then buy the Wimpy AV Player ($29) and embed it on your site to play the FLV files. site
But apparently you missed point 1, which was the more important point. Either get Flash MX Pro or Sorenson Squeeze. If you have Pro you can use Quicktime Pro or Final Cut (Express or Pro) and export your video as an FLV file. Problem solved.