Kimball's career began in the 1920s, when he performed with the Fate Marable Band on riverboats on the Mississippi. He later led a local group called the Gentlemen of Jazz.
In 1961, Kimball joined the Preservation Hall Jazz Band, the resident group at the newly opened Preservation Hall, a center for the traditional polyphonic jazz invented in New Orleans. Ben Jaffe, the hall's director, told the AP that Kimball's vocal performances of "Georgia on My Mind" were a highlight of the group's performances, invariably prompting standing ovations.
Kimball last appeared with the Preservation Hall Jazz Band in 1999.