mplayer lets you call it with "-input file=name_of_pipe", causing it to read commands from that file. If it's a named pipe, that can be a convenient way of sending commands to mplayer.
But it occurs to me that you may be able to do some fancy things by making calls to ChumbyNative methods. For starters, call _pipeOpen() from Flash and call mplayer, and then call _pipeWrite() to send it commands. E.g. to play /mnt/storage/movie.avi, you'd call:
mplayer = _pipeOpen("/mnt/storage/mplayer /mnt/storage/movie.avi")
And then to pause the movie, you'd send a single Space character by calling:
_pipeWrite(mplayer, " ");
Or to quit, call:
_pipeWrite(mplayer, "q");
If you wanted to be really fancy, you'd call _setDisplay(1) first, and then fiddle around with chromakey and alpha to overlay your controls on top of the movie player behind your Flash widget.
Of course, this all assumes your widget is running as the master instance, which is what you get when you run stop_control_panel; chumbyflashplayer.x -i /path/to/your/widget.swf