For the US, according to section 4-1-11 of the AIM (Designated UNICOM/MULTICOM Frequencies) for private fixed-wing flights you should use 122.75:
Air-to-air communication (private fixed wing aircraft): 122.750
Air-to-air communications (general aviation helicopters): 123.025
Aviation instruction, Glider, Hot Air Balloon (not to be used for
advisory service): 123.300, 123.500
I have no idea what the military does and their tactical comms might even be encrypted anyway, but they frequently use UHF instead of VHF, at least in the US.
Nor do I know what to do if you have two formation flights at the same time, but I guess that in reality it's either an air show with some form of semi-official control and perhaps even NOTAMs, or it's something private and in that case people make their own arrangements, e.g. picking some frequency that doesn't overlap with any nearby assigned frequencies. Using 123.45 is apparently common, but definitely not official.
Non-VHF communications for private flights would be regulated by the FCC, not the FAA, and personally I'm not sure if the benefits would be worth the extra equipment and the risk of confusion, but then again I know nothing about formation flying.
There's some useful information from the FAA in this policy order clarifying the use of 121.5 and 123.45. It says that 123.45 is for operational use in oceanic regions, and within the US it's reserved for "non-government flight test operations". There's also an FAA document on requesting temporary frequencies for airshows etc. but it's air to ground only.