Flagello was born in New York City, and studied at the Manhattan School of Music, where he was a pupil of Friedrich Schorr and John Brownlee. He also studied at the Santa Cecilia Conservatory, in Rome, Italy, with Luigi Ricci. Flagello made his professional debut at the Empire State Festival, in Ellenville, New York in 1955, as Dulcamara in L'elisir d'amore. He made his Metropolitan Opera debut on November 9, 1957, as the Jailer in Tosca. Four days later, as a last minute replacement, he sang Leporello in Don Giovanni. He quickly became a favorite with the audience in comic roles, such as Bartolo in The Barber of Seville and Dulcamara in Elisir d'amore, though he also excelled in more lyrical and dramatic repertory. In his 27 seasons with the company, he sang, notably, Rodolfo in La sonnambula, Giorgio in I puritani, Raimondo in Lucia di Lammermoor, Silva in Ernani, Wurm in Luisa Miller, Sparafucile in Rigoletto, Fra Melitone in La forza del destino, Philippe II in Don Carlos, Pogner in Die Meistersinger von Nürnberg, Timur in Turandot, and other roles. He created the role of Enobarbus in Samuel Barber's opera Antony and Cleopatra for the opening of the new Metropolitan Opera at Lincoln Center on September 16, 1966. Flagello also enjoyed a successful international career, appearing frequently in Vienna, Milan, Berlin, London, and other places. Flagello possessed a dark and very rich voice with a remarkable upper register extending to high A. He left an impressive discography which includes Così fan tutte, opposite Leontyne Price, Tatiana Troyanos, George Shirley, Sherrill Milnes, under Erich Leinsdorf, Lucrezia Borgia, opposite Montserrat Caballé, Alfredo Kraus, Shirley Verrett, Lucia di Lammermoor and Luisa Miller, both opposite Anna Moffo and Carlo Bergonzi, Rigoletto, opposite Robert Merrill and under Georg Solti, Ernani, Ballo in maschera, Forza del destino, all opposite Leontyne Price. He also recorded Handel's Alcina and Bellini's I Puritani, both opposite Joan Sutherland. He also interpreted the role of Harapha in the famous Archiv recording of Handel's oratorio Samson (1968). In addition to his operatic career, he had a small role in the flashback sequences in The Godfather Part II (1974) as an impresario threatened by Don Fanucci.