I'm no expert on these...so take my comments with a grain of salt.

First, look inside and see if there is a tag that describes the item. Anything that was actual military issue would most likely have one. Look on the insert, too. It would say something like

Flight Cap, Leather, B6 (and probably have a mfg's name, too).

I'm skeptical that this is an actual military item judging by other leather caps I've seen. Also, the AAF stars on the side and the blue button don't look military. But I could be all wet on that.

A quick Google doesn't turn up anything similar. Ebay items for US military leather flight caps aren't going for a lot. Axis stuff appears to be far more valuable.

Good luck with figuring out what you have.