If this is just a request for the best songs of the Vietnam era (assuming this means the era of significant US military involvement, mid-60's to mid-70's), we're talking about a lot of material. If we bring it down to songs about Vietnam, it's still a lot of material, but more manageable. In my view, some of the best were "Lyndon Johnson Told The Nation" by Tom Paxton, "Fortunate Son" by Creedence Clearwater Revival (John Fogerty), and "Born In The U.S.A." by Bruce Springsteen.
I know, people will agree with the first two, and think the last one proves me an idiot. It was written and released about nine years after the last American troops came home, and a lot of people think it's a celebration of American jingoism (Chrysler even asked Springsteen if they could use it in their commercials; he said no, even though I'm sure he could have charged them a bundle for the rights). My advice is to give it another listen, with an open mind and the words in front of you; I think it captures something pretty powerful if you can put your preconceptions aside.