Burnham graduated from George Washington University in St Louis, Missouri in 1909 and spend a year working with Glenn Brown there before moving to Birmingham. He opened his own office in the Comer Building in 1917. In 1933, during the Great Depression, he went to work for the federal government. He returned to his own practice in 1936 and entered into a partnership of Burnham, Echols & Smith in June 1945.
- Avondale Park pavilion
- Dulion Apartments, 1920
- Hood-McPherson building (Ensley), 1926
- Ramsay-McCormick Building, 1929
- Walter Miller residence, 5343 7th Avenue South, 1937
- Hury Amusement Co. theater in Nashville, Tennessee