1. Download and install the latest nVidia drivers (270.61) as well as the latest SLI profiles.
2. Turn off your computer and disconnect it from all power sources.
3. Open your case and ensure your SLI bridge is connected securely. Also check that all of your hardware's power connectors are securely in place.
4. Close your case.
5. Connect your monitor to the GPU in the second PCI-e slot. Make sure it is connected properly.
6. Boot up your computer and go to the nVidia control panel.
7. Under "Manage 3D Settings", select the program settings tab. If you do not have a profile for Crysis 2, add one by browsing for the Crysis2.exe file in the bin32 folder for the game.
8. Set the SLI Rendering option to Alternate Frame Rendering 2. Apply changes and exit the nVidia control panel.
9. Start Crysis 2 and play SP and MP flicker free (even with v-sync disabled!)
I had tried almost every fix on these forums with no success but for some reason, these steps fixed it for me. I re-tested this on a friends computer who had the same flicker problem and it worked for him as well. I'm not sure why step 5 is necessary but it appears that using AFR 2 rendering and running the monitor from the second GPU are the key steps for correcting the rendering glitch that causes the flickering.
If you are a Crossfire user and have success with these steps, please post here or PM me so I can update the OP.
Good luck!