Burnham has published in American Heritage, The Washington Post, MHQ, Transition, Emerge, The Columbia Journalism Review, and Indian Country Today. Burnham has taught college-level writing, literature, and history at the University of New Mexico, the University of Massachusetts (Amherst), Sinte Gleska College, Johns Hopkins University, and, as a Fulbright fellow, at Cheikh Anta Diop University in Dakar. He is currently a Term Assistant Professor at George Mason University in Fairfax, Virginia.