I'm a Realtor in the Killeen area. I mostly agree with what @Joe Scaparra said. But would like to add some more thoughts about the area.
The post rentals opening up to soldiers - I don't know the entire reasoning behind it other than indeed there WAS a lot of vacancy on post due, I assume, to superior off post options for Soldiers. Opening up that housing presumably adds rental inventory, essentially, but that effect is already priced in.
There are a LOT of rentals, but there are a LOT of renters. 2/3 of the area's inhabitants are renters, the inverse of the national ratio. Also, frankly, a lot of those rentals are not well taken care of, either because of sub par landlords or property managers. If you take decent care of your area rental, vacancy should not be a major concern. I would budget 8% vacancy but I've been under 5% in my time owning both a SFR and fourplex.
It is a military town, and that is the primary economy, followed by healthcare, schools and call centers. But it is a lot larger town than I think some people realize. Killeen is the largest town between Dallas and Austin - larger than Waco, Round Rock, Georgetown, Pflugerville, Cedar Park... And that is not including the on post population, Harker Heights or Copperas Cove. There has been some significant infrastructure improvements in Killeen - specifically the expansion and designation of Hwy 190 as I-14. Anecdotally, I have seen a surge in commercial/retail investment in the last 12 months.
As for being overbuilt, that is possible. Killeen has seen a huge surge in population since 2001, growing from 80,000 to nearly 140,000 now. However that population growth hasn't put a lot of pressure on prices which have kept up approximately with the rate of inflation. I do think that is due to the builders in the area, which are very active (the average home sold in the area in the last year was built after 2000).
So, it is it's own market. I always recommend diversifying, but there are folks having good success with rentals in our area. If you have a little capital but not a lot of time, I might look at fourplexes/duplexes where you can get a 6-7% cap rate. If you have more time and are more involved, you can look at SFR foreclosures and target a very slightly higher cap rate (and higher rent bracket). If you are a full time investor, BRRRR, wholetailing and traditional buy and hold can work in our area, and I know folks who do all three. (Some flipping, but very little).