He probably would have gone to Vietnam actually. Unlike most other scumbags of his era (Cheney, Bush, etc.) he didn't game the system as easily as he could have. Did the limited amount of student deferments unlike Cheney. He actually got called up but if IIRC he actually had an semi-legitimate temporary foot injury when he showed up that got him a delay and then he lucked out by pulling a low number.
Of course, Trump had gone to a military academy as a teen and I think he's mentioned, in his bragging way about things you shouldn't brag about, that he might have liked to pursue it because he would be a badass soldier but you know he HAD to run the company and all.
In fact, considering all that, it's probably not far fetched to say he's a war hero.