Congress has no authority to make such a law, so how could delegated
Congressional authority lead to any such regulatory authority?

Here's a quote from the Cornell web page on military law:

-----snip--------
Congress's control over formation, organization and government of the
national armies is plenary and exclusive.
-----snip--------

You have failed to support your position, Greg, or to even know the
words.

I've given you the following
1) Statement by the FAA's general counsel's office
2) References to the FARs which contain military exemptions
3) FAR statements as to the applicability of the regs

All you've given me is statements based on your own authority.