After completing flying training at Randolph Air Force Base in San Antonio, Texas, and at Williams Air Force Base in Arizona, Arnold Braswell became a member of the 33rd Fighter Wing at Otis Air Force Base in Massachusetts, where he flew F-86 Sabrejets.
In 1951-1952, Braswell flew 155 combat missions in jet fighters as a member of the 49th Fighter Wing, Taegu Air Base, South Korea, and the 4th Tactical Fighter Wing at Kimpo Air Base, South Korea.
From September 1952 to September 1955, he was a flight commander and squadron operations officer in the 3600th Combat Crew Training Group at Luke Air Force Base in Arizona. When the U.S. Air Force Academy opened in 1955 in temporary facilities at Lowry Air Force Base, Colorado, Braswell was assigned as commander of one of the original four cadet squadrons and served in that capacity for three years.
In October 1958, he was again assigned to the 49th Fighter Wing, which had been relocated to Etain Air Base in France, where for a time he was deployed to supervise combat training of French, Danish and Turkish pilots in F-100 Super Sabre aircraft and then commanded the 7th Tactical Fighter Squadron at Spangdahlem Air Base in Germany.
Braswell returned to the United States in August 1961 to attend the Air Command and Staff College. He transferred to Washington, D.C., in July 1962 and was assigned to Headquarters U.S. Air Force in the Directorate of Plans, where he prepared recommendations to the Air Force Chief of Staff on joint planning issues. In August 1966, Braswell entered the National War College at Fort Lesley J. McNair in Washington, D.C. He graduated from the college and also completed his Master of Business Administration degree from George Washington University in 1967.
He began a one-year tour of duty in the Vietnam War in July 1967 as Director of Plans at Headquarters of the 7th Air Force, in Saigon. Though a staff officer and not required to fly, he voluntarily flew 40 combat missions, most of them in F-4 Phantoms.
Following his return from Southeast Asia in August 1968, Braswell became the director of operations for the 4th Tactical Fighter Wing at Seymour Johnson Air Force Base in North Carolina. He was again assigned to Air Force headquarters in August 1969 in the Office of the Deputy Chief of Staff, Plans and Operations, where he served initially as an Air Staff planning representative in Joint Staff planning conferences. In 1970 he was promoted to the grade of Brigadier General and assigned as deputy director for force development in the Directorate of Plans, and in February 1972, he became deputy director of plans. In February 1973, Braswell was promoted to the grade of major general and assumed command of United States Air Forces units based in Turkey, with headquarters in Ankara].
Braswell was assigned to Supreme Headquarters Allied Powers Europe, Belgium, as assistant chief of staff for operations from September 1974 to June 1977. In July 1977 he was promoted to Lt. General and returned to the United States as Director for Plans and Policy (J-5), Organization of the Joint Chiefs of Staff in the Pentagon. In June 1978, he became commander of Tactical Air Command’s 9th Air Force with headquarters at Shaw Air Force Base in South Carolina. In that position, he also served as commander of the Air Force units assigned to the Rapid Deployment Joint Task Force of the U.S. Readiness Command. In June 1981 he was appointed Commander-in-Chief of Pacific Air Forces, an Air Force major command, headquartered in Hawaii, which encompassed all of the tactical air combat units in the Pacific Theater.
The general in his Air Force career logged more than 5,500 flying hours, most of these in jet fighters.
He was promoted to lieutenant general July 1, 1977, with date of rank listed as June 28, 1977. He retired on October 1, 1983.