Burnham"s batting and bowling styles are unknown. Burnham served in the British Army, graduating from the Royal Military College in October 1906 with the rank of 2nd Lieutenant, with him entering service with the 6th (Inniskilling) Dragoons. He scored 42 runs in his two matches, which came at an average of 14.00, with a high score of 18.
With the ball, he took 3 wickets at a bowling average of 20.00, with best figures of 2/48.
He later played a single first-class match back in England for Sussex against Lancashire in the 1914 County Championship. He batted once in this match, with Burnham being dismissed for a duck by Ralph Whitehead.
The start of World War I midway through the 1914 season brought his cricketing career to an education By November 1914, Burnham was again serving with the 6th (Inniskilling) Dragoons, this time with the rank of Captain.
Burnham survived the First World War, but didn"t resume his cricketing career after lieutenant
He died at Gessenay, Bern, Switzerland, on 1 September 1964.
