to practice on a military post, you must have a state license. any state - doesn't matter which one.
so, to work at Fort Drum, NY, you can have a Missouri state license - so long as you are only working on Fort Drum, in a military capacity.
if you wanted to work off-post (moonlight) in a civilian capacity, you would be required to have the license for the state that you would work in.
if you are thinking about practicing in NY after getting out of the military, i assume you would either have to do the AEGD, or stay in the military for five years before you would be eligible to get a NY state license. (isn't the requirement for NY to have either completed a residency, or have five years of practice experience?)