I experienced the same issue after installing the 12.1 drivers today. Had some very, very old drivers before updating to 12.1 and I basically had to reinstall the old ones to remove the flickering.
In my case I downloaded the file which you can find here: http://www.msi.com/product/nb/GX64
Im on a MSI GX640 with a ATI Radeon 5850 Mobility card.
Hope this helps!