Schilling joined the United States Army in September 1939 as an aviation cadet and received his commission in the Air Corps upon completion of flight training in May 1940. The following summer, he became one of the original members of the 56th Fighter Group.
In his time in Britain, he became the sixth-leading ace of the 8th Air Force, scoring 22 and a half kills against Luftwaffe aircraft. On December 23, 1944, he downed five German fighters to become one of the 38 Army Air Force "Ace-in-a-Day" pilots. Schilling flew 132 combat missions in two combat tours with the 56th.
In 1950, he flew from Britain to Maine in the first nonstop trans-Atlantic flight by a jet fighter. For this flight, Schilling received the Harmon Trophy. In 1952, he took command of the 31st Fighter Escort Wing at Turner Air Force Base, Georgia, flying F-84 Thunderjets, and led a non-stop flight across the Pacific Ocean to Japan in Fox Peter One.
On August 14, 1956, while serving as Inspector General in the Strategic Air Command's Seventh Air Division, Schilling died in a car accident on a narrow, two-lane country road in England between RAF Lakenheath and RAF Mildenhall — Royal Air Force stations used by the U.S. Air Force. Colonel Schilling was driving a Cadillac/Allard sports-racing car; he, General Curtis LeMay, and other race enthusiasts had each purchased a model to form a stable for Sports Car Club of America events. On the day of the accident, he was driving to Mildenhall to meet at the Officer's Club with an Army lieutenant who had expressed interest in buying the car. At fairly high speed, he approached another car from behind, intending to pass. The cap he was wearing started to blow off and as he reached up to grab it, the car skidded sideways and struck the stone side-railing of a bridge at Eriswell in Suffolk, cutting the car in half at the driver's seat and causing the front of the car to topple into the stream below. Schilling died instantly. The day before his death, he had flown his last flight in a B-47.. At the time of his death he was on Temporary Duty (TDY) from the HQ of 7th Air Division at South Ruislip to RAF Lakenheath.
On March 15, 1957, Smoky Hill Air Force Base in Salina, Kansas was renamed Schilling Air Force Base in his honor. The Air Force Association's Award for Outstanding Flight, which Schilling won in 1952, was named for him after his death.