However, it is not known if he was barred from having a firearm for other reasons.
For example, under federal law, people who are declared mentally defective or who have been committed to a mental institution cannot buy a weapon. People addicted to a controlled substance are legally not able to buy a gun, and some domestic assault misdemeanors also carry a penalty against buying firearms.
It has not been confirmed whether Kinnunen fit into any of those categories.
However, even if he did, the enforcement of those prohibitions can be inconsistent, said Eric Ruben, an assistant professor of law at Southern Methodist University's Dedman School of Law.
When someone becomes disqualified from buying a firearm, law enforcement agencies must report the person to a federal database that tracks people who are prohibited from buying firearms. But that does not always happen, Ruben said.
"It's not just whether or not there was a technical prohibition, but also whether or not it was reported in the database and whether there is an effort to enforce those prohibitions," Ruben said.
For example, if a domestic assault is classified under a different charge, such as ordinary assault, it may not be reported.
And as long as private gun sales are allowed in Texas, none of those prohibitions matters, Ruben said. In private sales, the seller is not required to run a background check on the buyer.
"So long as people can engage in private sales that don't call for background checks, that's a pretty big loophole," he said.
Ed Scruggs with Texas Gun Sense said it seems obvious that Kinnunen should not have been able to legally purchase a gun based on his past behavior and criminal record.