Entering Primary Flying School at Brooks Field, Texas, Cook graduated from Advanced Flying School at Kelly Field, Texas in January 1924 and remained there as an instructor. That August he joined the Third Pursuit Squadron at Clark Field in the Philippines, returning to Brooks Field in September 1926 as assistant engineering officer and flying instructor at the Primary Flying School.
Entering the Air Corps Engineering School at Wright Field, Ohio in June 1929, Cook graduated a year later and was assigned to the Aircraft Branch at Materiel Division Headquarters there. He became an instructor at the U.S. Military Academy in June 1934, graduated from the Air Corps Tactical School at Maxwell Field, Alabama, four years later, and from the Command and General Staff School at Fort Leavenworth, Kansas, in June 1939.
Reassigned to the Materiel Center at Wright Field, Cook served with the Engineering Section of the Production Division becoming chief of the section in April 1942. That November he was named district supervisor of the Eastern Procurement District at New York City, and the following May returned to Wright Field as chief of the Production Division.
Ordered to the Southwest Pacific in June 1945, General Cook joined the Far East Air Forces on Okinawa where he established an Air Force Depot and directed Air Force supply and maintenance activities in that area. After cessation of hostilities he was sent to Japan to establish an Air Depot and to assume command of the Seventh Air Service Area Command. Going to Manila in January 1946, he assumed command of the Far East Air Service Command (later redesignated the Pacific Air Service Command).
Assigned to the War Department General Staff, Washington, D.C., in June 1946, Cook became deputy director of the Service, Supply and Procurement Division (later redesignated the Logistics Division). Returning to Wright-Patterson Air Force Base, Ohio in July 1948, he was named deputy director of Procurement and Industrial Mobilization Planning, Air Materiel Command, becoming deputy to the commanding general for operations a few weeks later, and director of procurement and industrial planning, Air Materiel Command, in September 1949.
Joining the United States European Command on April 1, 1954, Cook was deputy commander in chief, with Headquarters at Frankfurt, Germany, moving to Paris, France May 3, 1954.
Cook retired from the Air Force on June 1, 1956, and died on March 18, 1980. His decorations included the Air Force Distinguished Service Medal and Legion of Merit. He was rated a command pilot, combat observer and aircraft observer.