He sat in the House of Commons of Great Britain from 1720 to 1721, and then became a judge of the Scottish Court of Exchequer.
He was the oldest son of Sir Thomas Kennedy of Kirkhill and Dunure (Lord Provost of Edinburgh from 1685 to 1687) and Agnes Halden.
[2] Kennedy was joint Solicitor General for Scotland from 1709 to 1714, sharing the office with Sir James Stewart, 1st Baronet.
He was appointed as Lord Advocate in March 1714, but he was dismissed in October 1714 after George I succeeded to the throne.
He later supported the 2nd Duke of Argyll, who organised his return at a by-election in January 1720 as Member of Parliament (MP) for Ayr Burghs.