Born in Cincinnati, Ohio, Kinneary graduated from St. Xavier High School in 1924,[1][2] and received a Bachelor of Arts degree from the University of Notre Dame in 1928 and a Bachelor of Laws from the University of Cincinnati College of Law in 1935.

He served as a captain in the United States Army during World War II.

[3] Kinneary was nominated by President Lyndon B. Johnson on June 28, 1966, to a seat on the United States District Court for the Southern District of Ohio vacated by Judge Mell G. Underwood.

He took inactive senior status on August 31, 2001, at which time he was the oldest actively serving federal judge.

His service terminated on February 14, 2003, due to his death in Upper Arlington, Ohio.