If you are running Compiz, there's your answer. Right now the DRI framework does not allow direct rendered output to be redirected through the compositor, so both OpenGL and Compiz draw to the same screen area and the result is flicker.
- turn it off (easy, drastic)
- use the "don't unredirect full screen" Compiz option to avoid flickering with fullscreen apps
- wrap your 3d or video app in a script which disables compiz while running then restarts it automatically when done
Kristian's blog has some info about the solution for this -- DRI2 -- but he doesn't have an entry covering the fact that everything he checked in had to be ripped out and redone when the underlying memory manager changed from TTM ot GEM. The DRI2 support is starting to go back in again now but there is still a bunch of work to be done before the framework is there and ready for us to start modifying the Catalyst driver to work with it.
I have the same problem with video flicker. I have read many, many possible solutions, entered wads of commands into my terminal, fiddled, twigged, and diddled with my ATI drivers, etc. and have come to the following conclusion: The flicker is NOT just with ATI cards and drivers. It is something inherent in Compiz desktop. The easiest solution I have found is to install the Compiz fusion icon, which is just a quick easy way to switch from the Compiz desktop to the Metacity (or other) less fancy desktop. One, clik, a 1 second flicker, and I am watching flicker free video. When I want to go back to the fancy desktop, a clik, a second of flicker, and I am back to my fancy schmancy Compiz desktop. I can't remember where I found the Compiz fusion icon, but, just google it, install it, and your video flicker problems is manageable.