USAF = US Amphetamine Fools

Where in 14 CFR, Part 91, et. al., does it authorize you to attach a
fully automatic machine gun on the aircraft, or a nuclear weapon, or
napalm, etc.,?

There doesn't need to be an authorization. There is no prohibition.

There are numerous exemptions in the FARs for military aircraft, and
there are a number of other blanket exemptions such as "Unless
authorized by the administrator".

The Administrator is capable of issuing exemptions for just about
every reg there is, and most likely has done so for the military. But
Part 91 gives the Administrator the right to do so.