Can I get a civilian drivers license with a military drivers license?

Yes. Had a soldier do this very thing. Just take your military license, the memo from the CO, and bingo. They’ll send you out the door with a paper copy, and send your real one in the mail.

He did his in the DMV office at the TJ mills gage visitor center.

It is a possibly, however be aware that Texas just recently changed its driver's license procedures. This past June I renewed my license and was surprised to find that they wanted proof of citizenshipship. They required either a raised seal birth certificate or my current passport. I had to go back home and get my birth certificate. I believe this is a state sponsored proof of citizenship for voting purposes but the lady at the counter would not answer my questions about why this change had came into effect. Then this past December same procedure for my wife to update her Texas driver's license as well. I bring this up for two reasons; first to save you a trip back to get your proof of citizenship. Second. If they changed this proof of citizenship aspect they may have made other changes as well. Such as no longer accepting military driver's license to issue Texas license. I know they used to do it many years ago as I did it for a young soldier in my section in the 1990s but that was a long time ago.

Only a DMV official can give you a correct answer.