Ex-airman Kelly 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.
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In a statement on Monday, 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 should not legally have been allowed to own a firearm, after having been denied a gun owner's permit by the state.
How did Kelley obtain a gun?
Analysis by Anthony Zurcher, BBC News, Washington
He was kicked out of the US Air Force, but how it happened may be important in understanding how he was able to purchase the weapons he used to kill 26 individuals in Sutherland.
Individuals who have been dishonourably discharged from the US military are prohibited from possessing firearms. Kelley had a "bad conduct" discharge, which is a level below "dishonourable" and didn't automatically qualify for a ban.
Kelley received his discharge because he was convicted in a military court of assaulting his wife and child, which - under federal and Texas law - could have been deemed a domestic violence incident that would have prevented him from purchasing a firearm.
In addition, if the conviction was classified as a felony, that too would have been an automatic disqualification.
The key, it seems, is translating a court martial verdict into its civilian equivalent. A prison sentence of a year or more, which Kelley received from the military court, is also grounds for a gun-ownership prohibition.
None of this apparently came up on Kelley's instant background check when he sought to buy firearms from a sporting goods store in Texas, however.
Kelley also did not disclose details of his military criminal justice record on his purchase paperwork.
Mother-in-law argument
Kelley was armed with the semi-automatic rifle and two pistols when he attacked the First Baptist Church of Sutherland Springs during Sunday services.
They say he had argued with his mother-in-law before the rampage, officials say.
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 Freeman Martin, the regional director for the Texas Department of Public Safety,
"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," Mr Martin added.
Who were the victims?
Wilson County Sheriff Joe Tackitt said between 12 and 14 children were among those killed in the attack in Sutherland Springs, a small town 30 miles (50km) south-east of the city of San Antonio.
The youngest of those who died was only a year old.
As many as eight members of the Holcombe family were killed in the shooting, the Washington Post reported.
The BBC spoke to the Holcombes' neighbour Pauline Garza, who said the family did not come back from church.
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The First Baptist Church's pastor, Frank Pomeroy, told US media his 14-year-old daughter, Annabelle, was among those killed.
Twenty people were wounded in the attack.
Who was the gunman?
Kelley was court-martialled in 2012 after he was accused of assault against his wife and step-son. He was sentenced to 12 months' confinement.
He received a "bad conduct" discharge two years later, according to Ann Stefanek, a US Air Force spokeswoman.
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Gov Abbott said: "It's clear this is a person who had violent tendencies, who had some challenges, and someone who was a powder keg, seeming waiting to go off."
Kelley worked till last July as a security guard for an amusement park run by the Schlitterbahn company in New Braunfels near Sutherland Springs.
His employment was "terminated" after just over five weeks, the company said.
He had a licence to work as an unarmed security guard, a job that police described as "similar to a security guard at a concert-type situation".
"There were no disqualifiers entered into the national crime information database to preclude him from receiving a private security licence," police said.
The shooting comes just a month after a gunman in Las Vegas opened fire on an outdoor music festival, killing 58 people and wounding hundreds in the deadliest mass shooting in recent US history.
[BBC SOURCES]
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