After earning a bachelor's degree in geological engineering from the University of Oklahoma in 1960, he was commissioned as a second lieutenant in the United States Marine Corps.

Dunham served four years in the Marines, then returned to the University of Oklahoma to complete an MBA in 1966.

Dunham was previously a board director of DuPont, Phelps Dodge, Pride International, Union Pacific and Louisiana-Pacific.

He was a director of the American Petroleum Institute, the U.S.–Russia Business Council and the Greater Houston Partnership.

Anderson Cancer Center, the board of trustees of the Houston Symphony, the George Bush Presidential Library, and the Smithsonian Institution.