Speicher's father had been a fighter pilot in World War II and went on his first airplane flight when he was five years old. Speicher was a cadet member of the Civil Air Patrol as a teenager. Upon graduation from FSU, Speicher joined the United States Navy and attended Aviation Officer Candidate School at Naval Air Station Pensacola, Florida. After flight training at various bases, he was designated as a Naval Aviator and spent several years as both a fleet squadron aviator in the A-7 Corsair II and F/A-18 Hornet and as a flight instructor on the F/A-18 Hornet.