The cousin of British actors Arthur Chesney and Edmund Gwenn, Jack Kellaway was one of six siblings who carved out careers in the entertainment profession. During the mid-to-late 1920s, he was largely associated with the Nat Phillips's revusical troupes Stiffy and Mo and Stiffy and 'Erb. In the latter troupe, he appeared opposite Phillips as 'Erb. His brother, Alec, was also an occasional member of both troupes during the same period.
Jack Kellaway was possibly born in England, along with another brother, Leon (a dancer who came to Australia with Anna Pavlova's ballet company). At least two other brothers, Alec and Cecil, were born in South Africa, where it is believed the family resided for some years. While little is known of their parents, it is likely that they were also involved in the theatre as it has been said that the Kellaways were South Africa's equivalent to the Barrymores. The most successful member of the family was Cecil, who spent more than two decades in the British and Australian film industries (seventeen years in Australia) as an actor, writer, and director before moving to Hollywood. In 1948, he garnered an Oscar nomination as Best Supporting Actor for The Luck of the Irish. One of the last films he appeared in was Guess Who's Coming to Dinner (1967) as Monsignor Mike Ryan.
Jack and Cecil followed Leon to Australia around 1920/1921, with Alec arriving in 1923. In 1925, prior to teaming up with Nat Phillips, Jack Kellaway toured the Fullers' circuit with F. Gayle Wyer's Bandbox Revue Company, appearing in revusicals alongside variety veterans such as Billy Bovis and Walter Cornock. Sometime around 1926, Jack and Alec joined Phillips's Whirligig Revue Company, with Jack taking on the role of Stiffy's onstage partner 'Erb, replacing Roy Rene's 'Mo'. Jack played the character in numerous adaptations of the Stiffy and Mo shows staged by the Whirligigs (ca. 1926-1927). Alec Kellaway later became Roy Rene's producer at the Tivoli.
Jack Kellaway remained with the Stiffy and Mo troupe after Phillips and Rene reunited in February 1927. Although it was initially announced that the shows would be based around the trio of Stiffy, Mo, and 'Erb, his position slipped back to support status soon afterwards. In early 1929, he returned as Phillips's partner following the disbanding of the Stiffy and Mo company. He was again joined by his brother Alec, who temporarily replaced Dan M. Dunbar, while the eminent vaudevillian was struck down by a lengthy illness.
During the 1930s, Jack Kellaway was associated with J. C. Williamson's, appearing in such productions as The White Horse Inn (His Majesty's Theatre, Melbourne, July 1934). He is also known to have worked a vaudeville act with his wife Sylvia in London in early 1931 (Coliseum, beginning 3 January 1931).