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.
When I read this post I thought "bloody ****" what a good point! So I looked at my iPod touch and iPhone to see if the cover was still on mine, " unfortunately" they weren't so it didn't help me resolve the dark pictures I'm getting on both devices. I have had the flash on and a home back light and have even reset reboot but the problem still exists. Wish Apple would sort it out in the next update, it's a real pain, even when I edit the photo from the photos folder the contrast and brightness is improved but the photos are still way to dark.