Duke was a native of Ennis, Texas and earned his undergraduate degree at Texas A&M University and a divinity degree at the Southwestern Baptist Theological Seminary in Fort Worth, before reconsidering his career choice and earning his medical degree at the University of Texas Southwestern Medical Center at Dallas.
He joined the faculty of the 2-year-old University of Texas Medical School at Houston in 1972. In the mid-1970s, he founded the Life Flight air ambulance service in Houston. His medical reports aired for years on KATV/Channel 7/Little Rock.