I have the game fully up-to-date and my AMD drivers are the latest, but I'm still getting flickering. The flickering is different than what it was before the patch was released that was supposed to fix it though. The flickering is now the entire screen flickering tinted black with lines running through it. There are also weird shaded shapes bouncing around. Performance also doesn't seem like it's where it should be.

I tried renaming the .exe to rift, fear or bioshock but I get bad performance and other issues.

I tried to take a screenshot of the flickering and weird things flying around but they all turned out blank. I took the screenshots with MSI Afterburner.

Here are my specs:

i7 920 @ 4.1
Crossfire 5870's
12GB of RAM

Please help.....

Install Catalyst 11.1, will work.

did you download catalyst profiles? I think that's the key to avoid the game flickering.
here's the dl link: http://sites.amd.com/us/game/downloads/Pages/crossfirex-app-profiles.aspx

Just set the brightness down by one increment and then raise it by one and it'll rectify the flickering issue (no im not trolling, it actually works).
That said if you're still getting flickering it might suggest that having CFX enabled is actually impeding the smoothness of ur gameplay (even if the reported frames are higher) so you might want to investigate disabling it in Catalyst just to check things out