Why won't shutter release when in flash mode?

The only thing I can think of, isn't related to the flash, but to the "confirm focus before shutter release" setting. My logic being you're using flash in a dark environment without an AF lock possibly.

Auto focus is the culprit here. switch to Manual focus and the shutter will fire :)

I had a similar problem with the Godox flash I attached to my d7500. It turns out that the contacts on both the flash and the hot shoe were dirty enough to cause a problem. A few seconds of light burnishing with some very fine steel wool solved it--taking care to blow away the residual dust and debris. I wouldn't do this every day, but if you leave the flash mounted for long periods, it may be necessary once in a great while. The before and after difference wasn't visible to me, but the flash started working normally after the "treatment."====