The key question, one which your DS can research in applicable Service postgrad education policy/regs/instructions, is whether the Service will pay for an additional degree of the same level, regardless of how the first was obtained.
If a member obtains a degree on own dime, duly reports it for service record purposes, there may be regs saying the member is now ineligible to use Tuition Assistance or be given full duty orders to a military post-grad school, war college or civilian school - for the same level of degree. The needs of the Service trump all. If it thinks an officer only needs 1 Master's, it only pays for one, and may not if the member already has one.
TA can be used for a PhD, and there are some small number of people who are sent full-duty for PhD. At USMA and USNA, there are special programs for officers who become permanent faculty there.
It will all be written down somewhere. In the Navy, a Master's is usually expected to be in the record no later than the O-5 (Commander) promotion board.
Now, as a boss of mine used to say, "unless a regulation came down from Mt. Sinai carved on a stone tablet, it can be changed or exceptions granted." If retention is down, and the officer is in a desirable branch/warfare specialty and year group, then things get looser. That also means what is true today may not be true 5 years from now. If there is an urgent need for X-degreed people, say, Cyber, and your DS is willing and available and a top performer, all kinds of waivers may fly, even if he has a Master's.
Degrees earned using Service time and/or Service money may have required "payback" tours in that specialty area, and may incur obligated service that may run concurrently during or consecutively after original obligated service.
Don't forget the Post 9/11 GI Bill for after separation. There are some strategies to stay in long enough to get the full benefit. That's one way to have Uncle Sam pay for things. This also requires research to see if the benefit will cover a level of degree already held.
http://www.benefits.va.gov/gibill/post911_gibill.asp
Taking the really long view, each individual state has its own Veterans Affairs department (names vary), which can also offer generous post-grad education benefits. Info will be on state websites.
There is nothing that says a member can't get the Service-supported degree first, and later, if member chooses to get another of the same level on own dime, all good.
I used a lot of "mays." That's just military reality. Needs of the Service - always the long pole in the tent. Change in policies, depending on those needs - also a reliable constant of military life.
The Services are in the business of growing operational commanders, who learn their warfare craft in operational tours, enriched by sufficient post-grad education that supports their primary warrior role. That's a usable insight for interview purposes.