Honestly it depends on the state you are trying to obtain the CCW in.....for example, Indiana requires no training time at all, where Nevada requires multiple hour of training time.
"DILLIGAF isn't an attitude, its a lifestyle, thats why its tattooed across my throat"
Most states that require training will most likely require you to show proof you were trained to fire a pistol along with your DD 214. Wyoming was allowing the DD 214 only for a bit but now requires some proof you were trained as well.
I had to present my DD214 to get my CHP, only to prove that I did not have a dishonorable discharge, which is viewed on the same level as a felony conviction, and prevents you from getting a CHP.
Besides a DD214 does not indicate the vet has any training or abilities with a firearm. I was in the Navy, and was never issued a firearm of any kind. My rating dealt with a lethal weapons on a totally different scale, measured in megatons. We maintained and kept the genie in the bottle, the genie that Albert Einstein first figured out was possible.
The OP is not asking about standard training to get a regular CFL. I'm MS you do not need to take a class to get you license. You have to fill out and notarize the paperwork, turn it in, pay your money, and wait. You'll be run through the FBI database and the local sheriff gets a copy of the app to check for warrants also.
We have an extra endorsement called a "Enhanced Carry" endorsement. You have to take a safety class approved by the DPS of MS and you are given a sticker on the back of your CFL. This is only valid for MS residents.
This endorsement allows you by law to carry in any normal place listed off limits to regular license holders with the explicit exception of jails, police stations, court rooms in session, and "places of nuisance" which in MS are defined as places where illicit gambling, drug use, prostitution and such are happening.
I'm honestly not sure what the military training you mentioned involves but I don't think it counts toward the enhanced. You can look on the DPS website at the list if enhanced instructors and ask any of them about that in particular.
The short answer is no, unfortunately. The way the law is written for enhanced, you have to go through a class. Part of the requirement is understanding the specifics of the enhancement. Are you in the Jackson area? Action Firearms Training (you can find them on Facebook) does a 2-night course with 1 in class and a night shoot on the range. They run $120/person plus ammo.