Denham attended private schools in his home parish and also spent a year in public school in Baton Rouge. He enrolled as a "subfreshman" at the Louisiana State University and A&M College in 1895 and, after withdrawing for a time due to illness, completed a bachelor of science in architecture in 1900.
Denham married the former Laura Eubank McNeill, daughter of a Methodist minister and Pensacola prohibitionist leader Hamilcar McNeill while a resident of Mobile. He is credited with designing additions to the Mobile City Hall in 1910 and was associated with Clarence L. Hutchisson and A. J. Downey in Mobile before 1916.
Denham was awarded a patent, No. 1,366,067, in 1921 for his design for an "aeroplane" with two horizontally-mounted propellers, giving the appearance of a helicopter.
In 1923 Denham joined with a relative and with E. B. Van Keuren in the Birmingham firm of Denham, Van Keuren & Denham with offices in the Age-Herald Building. By the end of that year the practice had moved to the Empire Building. In 1928 the firm split into Denham & Denham and a solo practice for Van Keuren, both located in the Comer Building.
- The Daily Picayune (June 28, 1900), p. 13
- Owen, Thomas McAdory and Marie Bankhead Owen (1921) History of Alabama and Dictionary of Alabama Biography. 4 volumes. Chicago, Illinois: S. J. Clarke Publishing Co.