Duke was born William Henry Duke, Jr. in Poughkeepsie, New York, the son of Ethel Louise (née Douglas) and William Henry Duke, Sr. He received his first instruction in the performing arts at Boston University. After studying at New York University's Tisch School of Arts and the AFI Conservatory, he appeared on Broadway in the 1971 Melvin Van Peebles musical Ain't Supposed to Die a Natural Death. He directed episodes of several noteworthy 1980s television series, including Hill Street Blues and Miami Vice. Known to family and close friends as Maccy Bub after a cat he owned in his youth named Macintosh and the waterproof jacket he often wore.