I'm having this problem too after changing to a new computer.
On my previous computer, I didn't have this problem, but I couldn't play movies (cinematics).
On my new computer, I can now play the cinematic videos, but the chat bar keeps flickering whenever the mouse crosses it.
I find that typing something or doing a quick voice command (press something like V, W, W) will stop the flickering, but the moment my mouse goes over the chat bar again, it starts flickering again.
Note that this isn't a problem with the combat log, but the entire strip of chat bar.