The reason I would flash the black is to get a cleaner line where the white traps to it. I would only set the job up this way if it was a relatively short press run.
With a small amount of trap, you can register the job in no time, and then flashing all the colors keeps it looking crisp. The amount of time you save on the registration process makes up for the extra time for the extra flash (on a short press run).
The cure temperature for ink is about 100 degrees hotter than the flash temp. If flashing causes it to burn a hole in the shirt, it's really going to burn in the dryer. I've never seen this happen with any kind of fabric...
As someone pointed out though, printing black directly on polyester might look a little funky next to the opaque white. Might look nicer to overprint it in this case.