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For my first academic LoR, I'll be using my Master's thesis advisor, so that's taken care of, but I'm not sure what to do for a second LoR. I'm in the military, and I'm currently an instructor at one of the military Staff Colleges. It's an academic setting, but would a letter from my school's director (equivalent to a Department Head in a typical university) be viewed as an academic LoR, or more of an employer LoR?

If I want a second purely academic LoR, one of my instructors from my Master's program expressed interest in writing one, but that was several years ago, we haven't kept in touch, and I suspect he was thinking more along the lines of recommending me for a physics PhD, rather than law school.

That sounds like more of an employment LoR, since you were working as an instructor. If you did any kind of significant academic research while working as an instructor, then that could be construed as more of an academic one, but that would still be a bit iffy. If you've been out of school for a few years, I don't see any harm in having an employer LoR instead of an academic one.