A 14-year-old cousin, who was babysitting the victim and two younger children, heard the gunshot and found the boy.
Kinney died at the hospital.
Police say the shooting is considered an accident.
"From the additional investigation, it appears that there was no criminal negligence," said Lt. Steven Prendergast of Gardena Police Department. "The case is still in investigation. As in any death of a child, we complete a full and thorough investigation, so it is still ongoing."
Police say it appears the gun was properly secured in the home, but that the boy somehow got his hands on it.
City News Service and the Associated Press contributed to this report.