As county champions Young Ireland represented Dublin in the 1891 All Ireland championship, but Kennedy shrewdly picked the best players from other Dublin clubs to augment his side. His decision paid off, with the Dublin side winning the county's first Leinster championship and going on to face Clondrohid of Cork in the All Ireland final. The final, which was held at Clonturk on 28 February 1892, ended with a Young Ireland victory in controversial circumstances. The Dublin side's fitness and tactical play allowed them to score 2–1 to Clondrohid's 0–2 in the first half. At this time a goal outweighed any number of points and for the second half Kennedy instructed his players to line the goalmouth to prevent Clondrohid from scoring. The tactic was successful and Young Ireland triumphed 2–1 to 1–9, despite failing to score in the second half. He went on to captain Young Ireland to a second All Ireland victory in the 1892 championship when they defeated Laune Rangers of Kerry 1–4 to 0–3, but was denied the possibility of a third consecutive win when Dublin boycotted the 1893 championship owing to a row over the central council's Parnellite stance. In 1894 he again captained the Young Ireland side to victory in the All Ireland final when they overcame Nil Desperandum of Cork after a replay. The replay, which was attended by a record crowd of over 10,000 supporters, actually ended in a draw, but the match was awarded to Dublin when the Cork side refused to play extra time.
Kennedy was a tall and powerfully built footballer who played mainly in the full back position and was renowned for his powerful running and kicking. He was most admired, however, for the intelligence and tactical acumen he brought to the developing game of football. The Young Ireland side's domination came to an end in 1895 when they lost the Dublin championship to Isle of the Sea, who refused to pick any Young Ireland players for the county team. He retired from the game after this disappointment and never played for the county again.