According to American Military News, Under U.S. Code, dishonorably discharged military personnel are not allowed to legally purchase a firearm and this is documented on the ATFs website. However the conditions of the dishonorable discharge have yet to be released. According to The Los Angeles Times, Federal law prohibits a person who has been dishonorably discharged from buying a firearm. Whether Kelleys discharge would trigger the law was not immediately clear.
However, Texas governor said on Monday to CNN that Kelley was denied a gun permit by the state. So how was it that he was able to get a gun? By all the facts that we seem to know, he was not supposed to have access to a gun, the governor asked.