The only option i can think of is to use Air and Nativeprocess as described here http://www.purplesquirrels.com.au/2013/02/converting-video-with-ffmpeg-and-adobe-air/
Otherwise I'm afraid this cannot be done unless someone does a port of FFMPEG to flash. The easiest way to do the video conversion you mention is to install FFMPEG on a server, send a request, and get the result back later.