There are number of reports in Apple support community regarding the front camera flickering issue during a FaceTime video call. Some reports indicate that when you use a white background the problem get much worse.
There apparently no permanent fix by Apple for this issue. The solution we provide is something that some people have confirmed working.
Update the phone to the latest version then, do a backup to your iTunes. Disconnect the phone from iTunes and restore factory settings. Restore the phone form the latest backup.