Slack went to the Conservatory in Chicago and worked from 1927 to 1931 in the Orchestra of Johnny Tobin. In 1931, he moved to Los Angeles, where he played in the bands of Henry Halstead, Earl Burtnett, Archie Rosate, Lennie Hayton and Ben Pollack. In 1936, he worked in the Orchestra of Jimmy Dorsey. Thereafter he played, from 1939, in the band of trombonist Will Bradley, who played in a Boogie Woogie style. Slack played the piano on Bradley's hit song "Beat Me Daddy, Eight To the Bar", named after the nickname of Slack, ' Daddy Slack '.
Slack founded his own Orchestra In 1942, which also played Boogie Woogie. The Orchestra got a recording contract with the newly founded Capitol Records and took, among other things, ' Cow Cow Boogie ' on, with vocals by Ella Mae Morse, that within a few weeks was a number one hit. It was the first million-seller by Capitol. This was followed by the hit ' Strange Cargo '. Slack took for Capitol until early 1950s plates on. He stopped in that time with his Orchestra and then went in a piano-duo or with his trio play.