It's not just the enlisted who support Trump. This is anecdotal, but my brother-in-law, a combat decorated and highly ranking Navy and Air Force (yes, both) officer and pilot (now retired), and his 25-year-old son, a West Point grad and Army Ranger who's seen combat in Afghanistan and is currently serving in Iraq, are both big-time Trump supporters. In fact, my nephew was wounded in Afghanistan and spent time at Walter Reed recovering. While there, he was invited by Trump himself to attend the inauguration, which he did along with his family. I've been around a lot of my nephew's West Point and Army officer buddies who have also voiced their support of Trump.
I don't understand it either, considering things like Trump's draft dodging and disparaging comments of McCain and the Gold Star family, etc.
One thing I do get, though, is that guys like my nephew who are regularly in combat situations appreciate the fact that Trump has increased spending on things they need to help them survive (e.g. body armor), and has changed the rules of engagement, which had gotten extremely restrictive under Obama -- to the point that it was endangering soldiers' lives. So that part, I understand. Otherwise, I don't get the love for Trump.
I also think, as others have mentioned, there is a lingering notion that began in the Vietnam era that Dems/Libs are anti-military/aren't patriotic/don't love their country as much as Reps/conservatives. Sometimes, that belief is passed down from one generation to the next, as is the case with my bro-in-law and nephew.