Kennedy was born into a family with a history of military service, and entered the navy shortly before the outbreak of the French Revolutionary Wars.

He spent some time in the East Indies, distinguishing himself in action, before returning to British waters and serving under a number of prominent naval officers aboard ships of the line.

[1] Thomas Kennedy differed from his brothers in embarking on a career in the navy, joining up on 12 August 1789 as a volunteer first class, under the patronage of Admiral Lord Hood.

[1][2] He was assigned to serve aboard the 74-gun HMS Colossus, which at the time was the guardship at Portsmouth, successively under the commands of Captains Hugh Cloberry Christian and Henry Harvey.

[1][2] He earned particular praise from Hyde Parker, the captain of the fleet under Admiral Lord Hood, for his role in bringing off 60 French civilians, mostly women, as the city fell to the republicans.

[1] He was promoted to lieutenant on 5 July 1796, while serving aboard Sybille, and went on to distinguish himself in January 1798 in an attack on a gunboat armed with five guns and carrying 50 men in the Bay of Manilla.

Terrible spent some time during this period as the flagship of Rear-Admiral Cuthbert Collingwood, and Kennedy served in the English Channel and in the Mediterranean.

[1] Both Kennedy and Harvey fought at the Battle of Trafalgar on 21 October 1805, in which Temeraire was second in line behind Lord Nelson's flagship, the 100-gun HMS Victory.

Fougueux's captain, Louis Alexis Baudoin, had suffered a fatal wound earlier in the fighting, leaving Commander Francois Bazin in charge.

[1][2] The draw-down of the navy in peacetime offered few opportunities for further service, but on 24 June 1834 Kennedy received a posting as Captain-Superintendent at Sheerness Dockyard.

[9][10][11] Kennedy received orders from the Admiralty in June 1838 to have Temeraire valued in preparation for her sale out of the service, and work began on dismantling her on 4 July.

She was then towed up the Thames to his yard, a voyage that J. M. W. Turner depicted in his painting The Fighting Temeraire tugged to her last Berth to be broken up, 1838.