He was "attempting to carry out death threats" against "his military chain of command", the report states.
The U.S. armed forces are required to report dishonorable discharges and misdemeanor assault charges to the FBI's National Instant Criminal Background Check System, that in turn would alert a firearms seller to deny purchase to any such offender.
Two U.S. senators, Republican Jeff Flake of Arizona and Democratic Martin Heinrich of New Mexico, said they planned to co-sponsor legislation aimed at ensuring that anyone convicted of domestic violence, whether in civilian or military court, would be blocked from legally purchasing a gun.
He entered a plea deal for a lesser sentence, but one which was still enough to prohibit him from firearm possession under federal law.
"We have initiated a review in the Air Force to figure out why his fingerprint records were not transferred to the database", she said.
Police documents say that Kelley managed to escape the hospital, though he was apprehended by two officers in El Paso as he was trying to get a bus ticket to take him out of state.
Kelley had also previously attended the First Baptist Church but was not welcomed there, Wilson County sheriff Joe Tackitt said.
NPR's Tom Bowman said, "This was mishandled by the Air Force Office of Special Investigations at Holloman Air Force Base in New Mexico, where Kelley was serving when he was arrested".
Kelley "was consumed by a dispute with his mother-in-law and spent time posting anti-God and pro-gun statements on Facebook in the months before the shooting", CNN reported, quoting officials, acquaintances and former classmates of the shooter.
After the devastating and troubling shooting at a Baptist church in Texas on Sunday, investigators, who looked into the background of the shooter, revealed he had a disturbing past of domestic violence.