Have you tried to interchange the CF Cable that connect the 3 Cards?
Use the one that you're using with the 2nd & 3rd card in place of the one that Connected 1 & 2. Remove the third card and see if the flickering happens with just 2 card and the 2nd CF Cable.
+1. No experience with Crossfire, but it sounds like the symptoms of a bad SLI bridge, that's exactly what happened to me.