Flanagan is the daughter of Rosanna (née McGuirk) and Terence Niall Flanagan, an Irish Army officer and Communist who had fought in the International Brigade in the Spanish Civil War against General Francisco Franco. Although her parents are not Irish speakers, they want Fionnula and her four siblings to learn the Irish language, thus she grows up speaking English and Irish fluently. She is educated in Switzerland and England. She trains extensively at the Abbey Theatre in Dublin and travels throughout Europe before settling in Los Angeles, California in early 1968.
Flanagan comes to prominence in Ireland in 1965 as a result of her role as Máire in the Telefís Éireann production of the Irish language play An Triail, for which she receives the Jacob’s Award in Dublin for her “outstanding performance.” With her portrayal of Gerty McDowell in the 1967 film version of Ulysses, she establishes herself as one of the foremost interpreters of James Joyce. She makes her Broadway debut in 1968 in Brian Friel‘s Lovers, then appears in The Incomparable Max (1971) and such Joycean theatrical projects as Ulysses in Nighttown and James Joyce’s Women (1977-1979), a one-woman show written by Flanagan and directed for the stage by Burgess Meredith. It is subsequently filmed in 1983, with Flanagan both producing and playing all six main female roles.
Flanagan is a familiar presence in American television, as she has appeared in several made-for-TV movies including The Legend of Lizzie Borden (1975) starring Elizabeth Montgomery, Mary White (1977), The Ewok Adventure (1984) and A Winner Never Quits (1986). She wins an Emmy Award for her performance as Clothilde in the 1976 network miniseries Rich Man, Poor Man. Her weekly-series stints include Aunt Molly Culhane in How the West Was Won (1977), which earns her a second Emmy Award nomination. She does multiple appearances on Murder, She Wrote. She plays Lt. Guyla Cook in Hard Copy (1987), and as Kathleen Meacham, wife of a police chief played by John Mahoney in H.E.L.P. (1990).
Flanagan makes guest appearances in three of the Star Trek spin-offs – Star Trek: Deep Space Nine episode “Dax,” Star Trek: The Next Generation episode “Inheritance,” and Star Trek: Enterprise episode “Fallen Hero.”
Flanagan guest-stars in several episodes of Lost as Eloise Hawking, a recurring character. She appears in such films as The Others opposite Nicole Kidman, Divine Secrets of the Ya-Ya Sisterhood as the eldest Teensy, and Waking Ned. She appears in television series and stage productions including the Emmy-nominated miniseries Revelations, starring Bill Pullman and Natascha McElhone, and in Transamerica, starring Felicity Huffman. From 2006–08, she plays Rose Caffee, the matriarch of an Irish-American Rhode Island family on the Showtime drama Brotherhood.