In 1968, Driscoll graduated from Aviation Officer Candidate School and received his commission as an Ensign (ENS) in the Naval Reserve. After initial flight training at Naval Air Station Pensacola, Florida, he completed advanced flight training at Naval Air Station Glynco, Georgia, and received his Naval Flight Officer wings in 1970. He was selected to be in the F-4 Phantom II as a Radar Intercept Officer (RIO). He was assigned to Fighter Squadron 121 (VF-121) at NAS Miramar, California, for fleet replacement squadron training in the F-4J, then to Fighter Squadron 96 (VF-96) The Fighting Falcons, also based at NAS Miramar. As a lieutenant junior grade (LTJG), he served as a RIO with his primary pilot, Lieutenant Randy "Duke" Cunningham. They became the Navy's only two flying aces during the Vietnam War while VF-96 was embarked on a Western Pacific deployment aboard the aircraft carrier USS Constellation.
Cunningham, with Driscoll as his RIO, made his first two kills on separate missions; his third, fourth and fifth kills occurred during a single day: May 10, 1972. The engagement became one of the most celebrated aerial dogfights in the war. After they bombed their intended ground target, they engaged 16 MiG interceptors that converged on a bomber convoy of USAF Boeing B-52 Stratofortresses attacking a railyard in Hải Dương. Cunningham shot down two MiG-17s, and became separated from the other aircraft in their strike package. The pair headed for the coast, where they spotted and shot down a lone North Vietnamese MiG-17. Their fighter was then hit by a missile, and they ejected over the Gulf of Tonkin and were rescued. Driscoll was awarded the Navy Cross for his actions.
During the war, Driscoll was promoted to lieutenant. Besides the Navy Cross, he was awarded two Silver Stars, a Purple Heart, and ten Air Medals. He was also nominated for the Medal of Honor.
Driscoll later became an instructor at the U.S. Naval Fighter Weapons School (TOPGUN) followed by his transition to the F-14 Tomcat and assignment as an instructor at Fighter Squadron 124 (VF-124), the F-14 Fleet Replacement Squadron for the Pacific Fleet at NAS Miramar (now MCAS Miramar), in San Diego, California. He separated from active duty in 1982, but remained in the United States Navy Reserve, flying the F-4 Phantom II and later the F-14 Tomcat in a Naval Air Reserve fighter squadron at NAS Miramar, eventually retiring with the rank of commander (O-5).