Though, it'd be a nice project to implement. Trigger the transcoding process via clicking the file's link, then maybe issue a small delay and redirect to a page with the resulting video file inside html5 <video /> tags. I guess I'm not sure if it will work like a proper 'stream' if the file is actively being transcoded and incomplete.
I'd think you'd also want to do some server-side session checking, to kill the transcoding process if the browser suddenly leaves the page. You might be better off asking these questions in the programming forum.