I don't know. He was convicted as a juvenile, in some states I believe that convictions as a juvenile are wiped clean upon reaching 18 or 21--totally removed from the person's record. In that case, yes, I believe he'd be able to buy a gun. It depends on Arkansas state law, and probably Federal law as well.
The thing to note here, of course, is not the Brady screed that "Second Amendment BAAAAAD," but instead to note that this person's conviction SHOULD stay with him for his entire life and prevent him from owning a gun. Obviously, the Brady folks just want to use this to deny all of us access to our Second Amendment rights.
}:-)4