Ok, that case has an extremly narrow opening for the camera and flash.
Try this. Take a flash picture at 2 to 3 feet with the case on and without the case on. Odds are you will see a big difference. And if you do, you have two choices. Modify the case or get a different case.
BTW is this a White or Black iPhone? Because the white ones tend to make the flash situation a tad worse.