Geni lists him as being the son of Isaac Chauncey.
CIVIL WAR HIGH COMMANDS has this to say about John S. Chauncey:
Born New York 8 March 1805. Midshipman USN 1 January 1812. (If these dates are correct this would mean that John S. Chauncey became a midshipman at age 7. He might have served with his father.)
Lieutenant 13 January 1825. Commander 8 September 1841. Dropped 13 September 1855. Captain USN 14 September 1855. (It would be interesting to know what happened here at this point in his life.)
Commander of USS Susquehanna June 1861. Promoted to commodore USN 12 March 1867. became Commodore USN (Ret) 4 April 1869.
Died Lewisburg, Pennsylvania 10 April 1871.