HDRs are actually 3 images merged into one. The three "bracket" images are under-exposed, default exposure, and over-exposed. If the camera flash was allowed it would distort the final results. Instead of the camera flash, try adjsuting Exposure Compensation to suit your preferences (drag your finger left or right, or tap on the Exp. button to see it's slider) -- this will shift all the of the HDR bracket images towards your exposure preferences.
Regarding your other question, why isn't the camera flash allowed during Auto and Pro mode capture, it can be enabled if you switch from DNG capture (a RAW image type) to JPG capture. DNG capture with camera flash has problems on some devices, and we're working with Apple to resolve this. Until then, we've disabled the flash on affected devices.