He grew up in Detroit, initially influenced by such pianists as Art Tatum, Teddy Wilson, and Nat King Cole, and then by bebop musicians.

Recordings under various leaders, including Giant Steps of John Coltrane, continued well into 1962, when he became vocalist Ella Fitzgerald's full-time accompanist.

After leaving Fitzgerald in 1978, Flanagan attracted praise for the elegance of his playing, which was principally in trio settings when under his own leadership.

[2][3] The family had a piano in the house, and Flanagan received lessons from one of his brothers, Johnson,[5] and Gladys Wade Dillard, who also taught Kirk Lightsey and Barry Harris.

[5][6][7] Flanagan graduated from Northern High School, which he attended with other future musicians, including saxophonist Sonny Red.

[8][9] Flanagan's early influences included Art Tatum and Teddy Wilson, both of whom he heard on the radio and playing in the Detroit area, as well as Nat King Cole and local pianists Earl Van Riper and Willie Anderson.

[13] Flanagan then played jazz and rhythm and blues with saxophonist George Benson in Toledo, Ohio, before being drafted into the army in 1951.

[13] After basic training in Fort Leonard Wood, Missouri, Flanagan auditioned as a pianist for an army show.

[5][16] Flanagan soon found work in clubs and studios, including recording Detroit – New York Junction with Thad Jones in March.

[5] Later that month, he returned to recording, this time with Miles Davis and Sonny Rollins, for tracks released on Collectors' Items.

[16] Rollins was leader for another session three months later: Saxophone Colossus,[7] which was labeled an "undisputed masterpiece" by The Penguin Guide to Jazz.

[18] Late in 1957, he was part of Miles Davis' band for a short period, before returning to Johnson early the following year, for another stay of 10 months.

[20] Another appearance on a landmark recording came in January of the following year: Flanagan was a member of the quartet that made The Incredible Jazz Guitar of Wes Montgomery; his playing complemented that of the guitarist, using controlled force on bebop numbers and delicacy on a ballad track.

[19] In this period, Flanagan recorded albums with several leaders from an earlier era, including Lionel Hampton, Jo Jones, and Pee Wee Russell, as well as one with Edison and around 10 with Hawkins.

[26] Later the same year, Flanagan left Fitzgerald and was part of Art Farmer's short-lived New York Jazz Sextet, which recorded Group Therapy.

[34] Prior to these performances, he had felt that his technique was inadequate for a soloist, but he enjoyed the extra exposure of being a leader, so decided to continue.

[39] In the early 1990s, Mraz was replaced by Peter Washington, whose heavier bass lines added urgency to the trio's sound.

[47] In late October 2001, Flanagan played in a John Coltrane tribute at the San Francisco Jazz Festival.

[2] The following month, he was admitted to Mount Sinai hospital in Manhattan; less than two weeks later, on November 16, he died there, from complications related to the aneurysm he had suffered a decade earlier.

"[35] In a review of a 1989 concert, Feather commented that Flanagan used "subtle dynamic shadings", while "bursts of upsweeping chords sometimes lent an element of surprise, with a nimble left hand offering graceful filigree fills" and occasional musical quotes that added humor.

[51] Other techniques he employed were, in Stanley Crouch's description, "crooning effects achieved by manipulating the pedals, holding down keys long enough to sustain notes in decisively different ways, and working out inflections that evoke the voice – sighs, moans, swells, purrs".