Is it currently possible to create a flash free live webcam chat with HTML5? If so, how can I go about doing this?
Purely with HTML5, it's just not going to happen right now.
That said, you could theoretically do it without a flash bridge, but there'd be some requirements. As it is, there are some command-line utilities for Mac OS that capture images from the iSight camera and upload them to a web server. Grabbing the images, and optionally sound, you could redraw to a canvas element a few times a second for a low-grade camera. I won't begin to guess about pushing audio. Use an AJAX stream to maintain the connection, and continuously push the new images to the canvas as they're uploaded.
The real question becomes this: Is it worth it? According to Adobe1, you might as well use a flash bridge. Unless, of course, you're intending iOS compatibility, which is a whole other ballgame on it's own.