That should be fine, but if you are in total CYA mode, then you could always ask to see a copy of his PCS orders stationing him in Kentucky. Those grant him a form of "dual residency," if you will, for the purpose of buying firearms. I used my military ID and a copy of my orders to buy several guns while I was stationed in Alaska with a Texas DL and CHL. When I came back home to Texas on leave, I'd simply use my DL and CHL to buy as normal.
Here's an excerpt from the ATF 4473 instructions page for dealer-to-peon sales:
If the buyer is a member of the Armed Forces on active duty acquiring a firearm in the State where his or her permanent duty station is located, but he or she has a driver’s license from another State, you should list the buyer’s military identification card and official orders showing where his or her permanent duty station is located in response to question 20.a
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Also:
Question 13. State of Residence:
The State in which an individual resides. An individual resides in a State if he or she is present in a State with the intention of making a home in that State. If an individual is a member of the Armed Forces on active duty, his or her State of residence also is the State in which his or her permanent duty station is located.
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