I have the same flicker problem with a single ati xfx 5970 black edition 4 gb gpu, and i made contact with ea and crytek but they really dont know what to do to fix it. I did found out that if you turn off the fullsrceen mode that problem is over but then you watching to those stupid windows bars. and they responded that i should turn of all background programs.... sometime i really think that those guy are thinking everyone is stupid in this world. So i told them that everything was turned of and i even send system files and screenshot to them and now still waiting for them to come with a solution but i think that there never will come one...
I also contacted xfx for personal support ( came with the black editon gpu
) they also are looking into it. to see if they can find a sollution.
Maybe some know how to fix the problem for the singel gpu configuration???
Running the game in windowed mode disables crossfire, so this isn't a satisfactory solution!
If you have Steam, try using radeon pro (http://www.radeonpro.info/en-US/Downloads/). You can then use FEAR as a crossfire profile. This should give you pretty decent scaling, not great though (I'm using a 5970 also).
If you have a normal retail copy, you can re-name crysis2.exe to rift.exe or fear.exe.