Duncan was born in Danville, Kentucky. He received his B.A. and M.A.degrees from Butler University and Columbia University Teachers College, respectively, before being appointed a professor of voice at Howard University in 1931. In 1935 he decided he couldn't perform Porgy and Bess at the National Theatre to a segregated audience. He worked with composer Gershwin, Ralph Bunche, and the Howard University Teachers Union to change this policy. The National Theatre backed down, and all were welcome to sit where they pleased for the production's brief run in 1935. The theater reverted to its policy of segregation immediately after, however, until citizen protests and ownership changes led to its desegregation in 1952. Porgy and Bess would later be criticized for its stereotypical depictions of African Americans.

Duncan also had a successful career as a concert singer, performing in more than 50 countries. His singing style, called by one historian “sweet, dreamy, aristocratic,” was well known nationally and internationally, and its echoes occasionally were heard in the voices of his best students. Duncan retired from Howard University in 1945 and continued to teach students in his basement studio while he was well into his 90s.