I'm having the same flicker issues with my 2008 Mac Pro with two ATI Radeon HD 5770 and four monitors. Updating to Yosemite has been a constant problem, primarily, but not limited to Safari (in fact, I had to copy paste what I had attempted to type in Safari to TextEdit, fixed several typos and then will repaste this back into Safari).
After reading a dozen or more posts on this and other sites about the Yosemite flicker, I have turned off all Safari extensions and plugins…as well as turning off and then when that didn’t work updating Flash.
I’ve had limited success, meaning everything will seem normal, ie, pre-Yosemite, for several minutes, but soon returns to the annoying flicker. Firefox, Opera nor Chrome have the same amount of flicker as Safari, but some pages still appear/disappear in parts and pieces. Filling in online forms is problematic…hard to figure out which box the typing is entering when the cursor and portions of the browser window flicker on and off as well as move positionally.
And the 10.10.1 update lessoned the amount of flicker but has not eliminated it.