Ex-airman Kelley was court-martialled for domestic violence in 2012, and was barred from owning or buying guns.
But last year he was able to purchase a rifle he used in Sunday's attack on a small church outside San Antonio.
He killed 26 people and fled the scene. He was later found dead in his car.
Police said he died from what appeared to be a self-inflicted gunshot wound after being chased by armed bystanders.
Kelley was also shot in his leg and torso by a citizen, the regional director for the Texas Department of Public Safety, Freeman Martin, was quoted as saying by the Associated Press.
In a statement, the Air Force said: "Initial information indicates that [Devin] Kelley's domestic violence offense was not entered into the National Criminal Information Center database by the Holloman Air Force Base Office of Special Investigations."
It said it was now - together with the Department of Defense - investigating the handling of Kelley's criminal records.
Texas Governor Greg Abbott earlier said Kelley, 26, should not legally have been allowed to own a firearm, after having been denied a gun owner's permit by the state.
Kelley bought the rifle from the Academy Sports + Outdoors shop in San Antonio. The store issued a statement sending "deep condolences" to the victims' families. -- BBC