I think ffmpegX can only convert flvs if you use certain exporters. I think you need to use one that uses mencoder rather than ffmpeg. It works for me when I use "MPEG 4 [.AVI] (mencoder)"
You could also try iSquint. I've heard it works.
But it seems like some (newer?) flvs are beyond all software at this point. I've encountered some that MPlayer, ffmpegX and iSquint just can't handle, even though the files play fine with the Flash plugin. I can't help you with those.