Kenney was born in Toronto, Ontario, the son of Mildred Agnes (Martin) and Herbert Kenney. Kenney established himself as a leading alto and baritone saxophonist and clarinetist in the 1920s as a member of the CJOR Radio Orchestra and as a sideman to Len Chamberlain at the Hotel Vancouver. The Western Gentlemen were first formed in 1931 as a result of an engagement at Vancouver's Alexandra Ballroom, for which he recruited trumpeter-pianist Glen Griffith, trumpeter Jack Hemmings, saxophonist Bert Lister and bassist Hec MacCallum, who would later be joined by drummer Ed Emel and vocalist-saxophonist-pianist Art Hallman. Following their CJOR radio debut in 1934, the band embarked on a three-year run at the Waterton Glacier International Peace Park in Waterton Park, Alberta, adopting as its theme song the 1922 Billy Hill-Larry Yoell waltz, "The West, a Nest and You, Dear".