[2] In May 1931 Kirby and his teammate and compatriot Norman Farquharson, were runners-up in the doubles final of the French Championships, losing in straight sets to the American pair George Lott and John Van Ryn.

Later in July Kirby beat his doubles partner in straight sets in the singles final of the Scottish Championships at Peebles.

[7] In 1934 Kirby reached the singles quarterfinal of the Wimbledon Championships but lost in four sets to American Sidney Wood.

[8][9] Later that same year at the U.S. National Championships he defeated future Grand Slam winner Don Budge in the fourth round to reach the semifinal in which he lost to eventual champion Fred Perry in four sets.

Kirby had a Davis Cup match record of 16 wins vs. 8 losses and was more successful in doubles (7–1) than singles (9–7).