0615 GMT April 24, 2018
Ex-airman Kelley was court-martialed for domestic violence in 2012, and was barred from owning or buying guns, BBC wrote.
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 AP.
In a statement, the US 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.
Kelley was armed with the semiautomatic rifle and two pistols when he attacked the First Baptist Church of Sutherland Springs during Sunday services.
He had argued with his mother-in-law before the rampage, officials said.
Kelley called his father after he was shot by an armed bystander and said he did not think he would survive.
"This was not racially motivated, it wasn't over religious beliefs," said Martin.
"There was a domestic situation going on with the family and in-laws," he said, adding that Kelley had sent threatening texts to his mother-in-law.
"We know that he expressed anger towards his mother-in-law, who attends this church," Martin added.
On Monday evening, a vigil was held in Sutherland Springs.