In 1933, he resigned to apply for appointment as a flying cadet, U.S. Army Air Corps.

He was appointed a flying cadet in February 1935, at which time he entered training at Randolph Field, Texas.

Afterwards, he was assigned to the 97th Operations Squadron, Mitchel Field, New York, as a flying cadet, in conformance with the personnel policy of those years which required an additional year of duty as a flying cadet subsequent to graduation and prior to commissioning.

From 1953 to 1957, he was assigned to various staff positions, including duty as an executive to the Under Secretary of the Air Force.

Then in June 1962, Burham was appointed director of special investigations, (The Inspector General.