Coats graduated from the U.S. Naval Academy in 1968 and was designated a Naval Aviator in September 1969. After training as an A-7E pilot, he was assigned to Attack Squadron 192 (VA-192) from August 1970 to September 1972 aboard the aircraft carrier and, during this time, flew 315 combat missions in Southeast Asia. He served as a flight instructor with the A-7E Readiness Training Squadron (VA-122) at Naval Air Station Lemoore, California, from September 1972 to December 1973, and was then selected to attend the U.S. Naval Test Pilot School at Naval Air Station Patuxent River, Maryland.