Thomas Kennedy was the 17th (!) child but only the second surviving son of Sir John Kennedy (d. 1742), 2nd Baronet of Culzean, and Jean Douglas (d. 1767). He was the older brother of David Kennedy, and a first cousin of the 10th and 11th Earls of Eglinton.
Although not known with certainty, he is likely to have attended the University of Glasgow, like his brothers. He inherited the baronetcy of Culzean on the death of his brother, John, in April 1744. Later that same year, in October, he served as an ensign in the British 33rd regiment in the Netherlands, striking up a friendship with fellow soldiers James Caulfeild, 4tj Viscount Charlemont, Francis Willoughby, 3rd Baron Middleton, and John Ward, later Viscount Dudley and Ward. In 1745, he purchased an army Captaincy, but left the army just a few years later to embark on a Grand Tour of Europe. The Grand Tour was extended several times, and he spent much of the next decade in Italy and France before returning, in 1755, to his native Scotland.
In 1758, John Kennedy (1700-1759), 8th Earl of Cassillis and Thomas's fifth cousin, died without issue, leaving his estate to Thomas and his heirs male, which marked the beginning of a major legal dispute. On 29 February 1760 the Court of Session found the right to the estates of the 8th Earl to be in Thomas' favour, after a competition, both for the estates and for the title of the 8th Earl of Cassilis, between William Douglas, Earl of March, and Sir Thomas. Thomas Kennedy never married, and upon his death in Edinburgh on November 30, 1775, was succeeded as Earl by his brother David.
A neighbour of the Boswells of Auchinleck. According to the Journal of Boswell's German and Swiss Travels, Sir Thomas had "talked to JB about the pleasures of being in Italy, where he had spent three years". In his journal entry for October 17, 1764, while visiting the court of Gotha, Boswell likened Sir Thomas to the Chamberlain of that court, C. G von Helmoldt.