FaceTime Front Camera Image Flickers

Problems like this are most likely in the software of the iPhone. When it happens with a MacBook camera, you can fix it most of the times by dumping the PRAM upon starting your computer (command option P R), but that's not possible on your iPhone of course. You can however try to simply reboot your iPhone, and that might even fix the problem. You reach the off-switch by holding the sleep/wake-button for several seconds.

If that doesn't work, we'll reach the next step for fixing most software-related problems: restoring your iPhone's software (what does not mean that you have to get rid of all your personal data). simply let iTunes run a full backup first, then click the restore-button on you iPhone information screen in iTunes. After restoring you will be asked if you want to put your data back, and the problem will probably be fixed.

If that does not fix your problem you might want to consider taking your iPhone to a Genius Bar (if available in your area) or send it back for repairs (if you are still in your warranty period).