Pissing into the wind here if you're asking for official tech support, seeing as it blatantly says AMD PEER TO PEER forums.
HD3870, HD4870, HD5850, HD5970, HD6850, HD6870, HD7850 and HD7870 cards have all been used here with that game, no "z-fighting" or flickering at all here either.
Plus, you provided a whole lot of information about your system components, operating system, configuration, game patch version etc, didn't you ?
Probably overlooked the STICKY FAQ thread which says to READ IT BEFORE POSTING as well as the fact that this is only a user to user based forum.