One other setting that will cause the Flash button to grey out is HDR. It is on screen 4 of the recording menu. Try turning it off and it might allow you to adjust your flash settings.
in my case i believe the preset i had that prevented the flash was the electronic shutter (actually, this and the seilent mode), so i turned it off and it worked. Luckyly enough the setup is on the same 4th recording menu as the HDR setting. Thanks for posting about this subject!