During World War II, Millsap served in the Army Air Corps as an airplane mechanic. Following the war, Millsap attended the University of Maryland and then law school at American University, graduating in 1952. Millsap also married the former Martha Vaughn, and the couple would go on to have two children, Brian and Carol.
Millsap then entered private practice, eventually becoming a name partner in the Falls Church law firm of Gibson, Hix, Millsap and Hansbarger with Lytton H. Gibson, William B. Hix and William H. Hansbarger.
On August 12, 1968, Millsap was appointed by Governor Mills E. Godwin to the 16th Judicial Circuit Court to replace John C. Testerman. Judge Millsap's appointment was confirmed by the Virginia General Assembly on March 12, 1969.
Following his retirement from the bench on October 1, 1983, Judge Millsap and his wife retired to Florida. Millsap's wife died in 2004, and he moved to Silver Spring, Maryland to be close to his daughter.
Millsap died in the Suburban Hospital in Bethesda, Maryland and is buried in Arlington National Cemetery.
- "Selection as Judge Serves Millsap as Birthday Present."Evening Star, 13 Aug. 1968, Three Star NIGHT FINAL, p. 23. NewsBank. Accessed 29 Sep. 2018.
- Schudel, Matt. "Burch Millsap, 85; Fairfax Judge Presided Over 'Roy Rogers' Murder Case." Washington Post. The Washington Post, 28 June 2009. Web. 31 Dec. 2013.
- Klose, Kevin. "Falls Church Lawyer Named to Circuit Court." The Washington Post, Times Herald (1959-1973): 1. Aug 13 1968. ProQuest. Web. 31 Dec. 2013
- "Suburb and State: Judge Confirmed." The Washington Post, Times Herald (1959-1973): 1. Mar 13 1969. ProQuest. Web. 31 Dec. 2013.