Originally Posted by raymor

You CAN convert your flv to mp4 with no loss of quality. Because flv video is nothing more than a package holding mpeg4 inside, you can strip off the flv package and be left with raw mpeg4, aka .mp4.

To do using ffmpeg:
ffmpeg -i "filename.flv" -vcodec copy -acodec copy "filename.mp4"

The magic is the "copy" part, which tells ffmpeg to just copy the video and audio with reencoding it. Once you have plain mpeg4, most anything will play play it because again all of the popular formats are packages for mpeg4, so most any player already knows how to play mpeg4 after unpacking it.