This is a bug from the driver. You installed the 13.4 WHQL right? I'm getting with flickers sometimes when I'm gaming (especially lol), this happens to my hd7950 and hd6670.
It could be that firefox gives the same flickers.
The other drivers don't have this issue as much, but I use these drivers because they fix the frame latency for smooth gaming.
Like I said, this WHQL driver isn't fully bugfree, the next official driver will fix this normally.