Burcham was born in Cadiz, Indiana, and grew up in Whittier, California in the eastern Los Angeles basin. Burcham sold burglar alarms of his own design to finance flying lessons from the O'Donnell School of Aviation in Long Beach, California, where he became chief instructor. In 1933, he set numerous upside-down flight endurance records that were broken much later by Joann Osterud. He flew his Boeing 100 to the World's Aerobatic Championship in 1936. In 1941 he joined Lockheed and rose to the position of Chief Pilot a few years later.
Burcham was killed in the flame-out take-off of a production prototype P-80 Shooting Star, America's first production jet fighter. He is buried in Forest Lawn Cemetery in Glendale, California.