I got the EVGA GTX 580 super-clocked, set up my new pc, and started having flicker/flashing with the main monitor. I tried changing power supplies, changing the cables and ports, and it always turns out to be the main monitor that flickers, right from the log-in screen. If use just one of the monitors it works fine. Drivers are up to date on all components, even the HP monitors, I installed the actual drivers for those specific monitors, not just generic PnP. The monitors are HP 25" 2511x running at 1920x1080p. Rest is fine:
ASUS p67m pro, i7 2600k, win 7 ultimate (64)
If you have two different monitors then it's most likely than first monitor doesn't support second monitor resolution/refresh rate. So you must set optimal resolution for each monitor individually. Doing so, it should work.
If you have same (brand/model) monitors and you have flickering on just one monitor, than honestly am not sure what can be the problem...
I personally had 2 monitors setup. One was Samsung 19" running at optimal 1280x1024 and second was LG 22" running at optimal 1920x1080. Different resolution setting for each monitor. I hope this helps. Cheers!