Particularly remembered as an accompanist of Ella Fitzgerald and player on Giant Steps by John Coltrane. He played on a number of critically acclaimed recordings, such as Sonny Rollins' Saxophone Colossus, The Incredible Jazz Guitar of Wes Montgomery , and Art Pepper's Straight Life .
Flanagan's style was both modest and exceptionally musical. He embodied many of the most important qualities associated with jazz: swing, harmonic sophistication, melodic invention, bluesy feel and humour. Interestingly, he appeared on a number of highly innovative albums. (His awkward solo, recorded on the extremely fast and harmonically complex title-track of Giant Steps, is an infamously rare instance of the usually unflappable pianist being caught off-guard.)
During his career, Flanagan was nominated for four Grammy Awards — two for Best Jazz Performance (Group) and two for Best Jazz Performance (Soloist).