The reduced rate for USPS flat rate Military boxes is only to APO/FPO boxes. If sent to a regular US address (such as Sailors have at A School), even in the Military box, it costs the same as a regular flat rate box.
If you have a good Post Master, he/she will help you determine the cheapest way to ship items. Sometimes it is cheaper to go with flat rate boxes and other times, it is cheaper to go with other boxes.
That's because the packages are not delivered directly to the students in their barracks rooms, they go to the mail room. Any package does, no matter how you send it. I don't know where his specific mail room is, but he should get a notice when it arrives, then he goes to pick it up. (mail room is not the same thing as the post office on base)
Two days to the base, then all packages must clear basic security, then it goes to the mail room which sends out a notice, then he has to go pick it up. USPS is slightly better as federal mail must be handled more strictly.
Does anyone have an address to the A school in Pensacola