After the war Kilburn worked for a Malone ice cream and candy wholesaler before beginning a career in banking. In 1930 he was appointed president of the People's Trust Co. of Malone. He was also a member of the board of directors of the Marine Midland Trust Company of Northern New York.
He was elected to Congress in 1940 to fill the vacancy caused by the death of Wallace E. Pierce and served from February 13, 1940, until January 3, 1965.