You can screen record it then upload it to Youtube. Although, I'm sure aeo has an export to video feature planned in the pipeline :P. If you could implement something along those lines, that would be super slick!
Unfortunately, video export is not in my areas of expertise. :( Someone else is welcome to try, though. The rendering code is readable. The converted replays look like this:
http://aesoft.org/pokemon/uploads/lampeskaerm-vs-Violatic--2011-04-26.txt
Barring that, I would recommend screen-recording and uploading to YouTube.