Thomas Lee Flanagan was born March 16, 1930, in Detroit's Conant Gardens neighborhood, the youngest of six children of Johnson Flanagan Sr., a postman, and Ida Mae Flanagan, a garment worker; both parents had come north from Georgia. He got a clarinet at six and switched to piano soon after, studying first with his older brother Johnson Jr. and then with the Detroit teacher Gladys Wade Dillard, who trained several of the city's future jazz pianists. Records by Art Tatum, Teddy Wilson, and Nat King Cole shaped his early ear, and once he heard Bud Powell he absorbed bebop's vocabulary directly into his playing. He graduated from Detroit's Northern High School already gigging around town.

Flanagan's professional life began around 1945, in a band led by trombonist Frank Rosolino, and by the late 1940s he was a fixture of Detroit's remarkably deep postwar scene, playing in tenor saxophonist Lucky Thompson's band alongside baritone saxophonist Pepper Adams and guitarist Kenny Burrell, and sitting in when Charlie Parker came through town. In 1949 he took his first regular chair at the Blue Bird Inn, the club that anchored the local scene alongside pianists Barry Harris and Hank Jones. The Army drafted him in 1951; he served through 1953, including a stretch in Korea as a motion-picture projectionist after auditioning successfully for an Army entertainment unit. Back in Detroit, he resumed at the Blue Bird until Barry Harris took over the house piano chair in 1954. In 1956, just before Flanagan and Burrell left for New York together, Savoy Records captured the scene's core players on Jazzmen: Detroit (Savoy MG-12083), a session pairing Flanagan and Burrell with Adams, bassist Paul Chambers, and drummer Kenny Clarke.

Flanagan and Burrell arrived in New York together in 1956 and roomed at Burrell's aunt's home in Harlem while they found their footing. The footing came fast: on March 16, 1956, his 26th birthday, Flanagan cut his only-ever studio session with Miles Davis, a Prestige date (later collected on Collectors' Items) that also featured Sonny Rollins; that June he was the pianist on Rollins's Saxophone Colossus, already regarded as a landmark; and that August he had his first stint accompanying Ella Fitzgerald, a booking of about a month that included the Newport Jazz Festival. From 1956 into 1958 he toured and recorded steadily with the J.J. Johnson Quintet, and it was on a European swing with that band that he cut his debut as a leader, Overseas (Prestige, recorded August 1957 in Stockholm with bassist Wilbur Little and drummer Elvin Jones).

The turn of the decade brought some of the most enduring sideman credits of his career. In May 1959 he played on John Coltrane's Giant Steps, memorably fumbling for a chorus on the harmonically brutal title track before recovering, a rare public stumble for a pianist critics otherwise called unflappable. In January 1960 he was the pianist on Wes Montgomery's The Incredible Jazz Guitar of Wes Montgomery. In 1961 he reunited with the Detroit crowd on Motor City Scene (Bethlehem), co-billed with Donald Byrd, Adams, Burrell, Chambers, and drummer Louis Hayes. He spent 1961 and 1962 touring and recording heavily with Coleman Hawkins, including a UK tour, and worked in a trio led by guitarist Jim Hall with bassist Percy Heath. A trio date from March 1959, cut for an unissued Blue Note session built entirely around West Side Story tunes, finally surfaced two decades later as Lonely Town (1979).

From 1962 to 1965, under an arrangement brokered by Norman Granz, Flanagan became Ella Fitzgerald's full-time accompanist, touring internationally including a 1964 trip to Japan. He stepped away in 1965 to work again briefly with Rollins and to join trumpeter Art Farmer's New York Jazz Sextet for the album Group Therapy, then spent part of 1966 accompanying Tony Bennett on the West Coast. In 1968 he returned to Fitzgerald, this time as pianist and musical director, a role he held for a decade, touring 40 to 45 weeks a year and playing his own trio sets within her concerts. He began recording as a leader again during this stretch, starting with Solo Piano (recorded 1974 in Zurich, later issued by Storyville) and The Tommy Flanagan Tokyo Recital (Pablo, recorded live in Tokyo February 15, 1975, with Keter Betts and Bobby Durham) - his first leader dates since the Overseas era.

A heart attack in 1978 prompted Flanagan to leave Fitzgerald's band and lead his own trio full-time for the rest of his career, and the recordings piled up: Eclypso and Montreux '77 (1977), Alone Too Long (1977), Our Delights (1978, a duo album with fellow Detroit pianist Hank Jones), Trinity (recorded 1976 with Ron Carter and Roy Haynes, issued 1980), and Tommy Flanagan Plays the Music of Harold Arlen (recorded 1978, released 1979). A single June 1983 session with Ron Carter and drummer Tony Williams - Flanagan's only recording with Williams - yielded two Japanese LPs, The Master Trio and Blues in the Closet. He paid tribute to his old Giant Steps colleague on Giant Steps (In Memory of John Coltrane) (Enja, 1982, with George Mraz and Al Foster) and to Thelonious Monk on Thelonica (Enja, 1983); both earned Grammy nominations, as did The Magnificent Tommy Flanagan (1981, with Mraz and Foster). His long-running trio anchored by Mraz gave way in the early 1990s to one with bassist Peter Washington, and in 1991 he closed the circle on Beyond the Blue Bird (Timeless), reuniting with Burrell to revisit the Detroit club where they'd both started. Later that year a collapse led to quadruple bypass heart surgery and, subsequently, treatment for an aneurysm; he kept touring and recording regardless, including Jazz Poet (1989, with Mraz and Kenny Washington) and, after his health scare, Sea Changes (1996) and the live Sunset and the Mockingbird (recorded at the Village Vanguard on his 67th birthday, March 16, 1997; released 1998 on Blue Note), both earning Grammy nominations for individual tracks. He won the Jazzpar Prize in 1993 and an NEA Jazz Masters fellowship in 1996, and toured Japan repeatedly with the all-star "100 Golden Fingers" piano troupe. In October 2001 he performed a Coltrane tribute at the San Francisco Jazz Festival; he was hospitalized soon after at Mount Sinai and died November 16, 2001, in New York, of complications from an aneurysm, at 71. A track from a posthumously released 2001 birthday concert, A Great Night in Harlem, earned him a further Grammy nomination in 2003.

Flanagan built his style on Art Tatum's harmonic richness, Teddy Wilson's clarity, and Bud Powell's bebop line, but his own voice was famously understated: swinging, harmonically sophisticated, melodically inventive, and laced with blues feeling and dry humor rather than pyrotechnics. "I like to play like a horn player, like I'm blowing into the piano," he said. "The sound of a piece - its overall tonality - is what concerns me." Critic Whitney Balliett noted his habit of stating a melody through "dissonant, levering chords played offbeat or staccato"; Leonard Feather praised his "subtle dynamic shadings" and "bursts of upsweeping chords"; and Stanley Crouch pointed to voice-like effects, "sighs, moans, swells, purrs," achieved through pedal control. He favored the songbooks of Duke Ellington, Thelonious Monk, Tadd Dameron, Benny Golson, and Thad Jones. Best known publicly as the most trusted accompanist of his generation, first to Ella Fitzgerald and briefly to Tony Bennett, he was equally in demand as a studio sideman on some of the era's defining records, and his rare on-record miscue on Coltrane's "Giant Steps" only underscored how reliable he otherwise was. Younger pianists including Kenny Barron (who called him his "hero"), Kirk Lightsey, Alan Broadbent, and Helen Sung cited him as a direct influence, and he remained a close contemporary and mutual influence of fellow Detroit pianists Barry Harris and Hank Jones throughout his career.