i noticed my iphone 5 has this problem too.
i can usually take one picture where the flash is in sync and then every subsequent picture is out of sync. the only way to get it working again is to turn the phone off and then back on. it will then take a picture in sync with the flash and then go back to being out of sync after a while.
my iphone is a 16gb white version so i don't think the problem is hardware related.
The apple support suggested i should restore the phone but as many of you mentioned the flash sync problem occured again. I'm also not interested in exchanging my iphone 5 for a new one because everything else seems to be working great except the flash.
The flash itself is also great in case it works properly. I think that it must be a software issue.
Please Apple fix this as soon as possible.