Although he began as a tail-end batsman, Kennedy developed his defence so well that by 1921 he often opened the batting.
When he scored 101 against Kent in 1923, Wisden remarked "he was caution itself up to a point, but hit twelve fours".
Kennedy toured South Africa in 1922–23, where he did well on the matting pitches, taking 31 wickets in his only Test series.
The dry summers of 1933 and 1934 saw Kennedy's bowling decline, but he still played a vital role as Hampshire's stock bowler.
He retired to coach at Cheltenham College at the end of 1934, but returned to the Hampshire team during the school holidays and bowled effectively – aided by the new leg before wicket law – taking seven for 46 against Northamptonshire, and six for 94 against Essex.