As a college undergraduate she studied biochemistry but after graduating and working in her field, she enrolled in the Sydney Conservatory, where she said it was "so blindingly obvious" that singing was her "true pathway." She was accepted at the La Scala Opera School in Milan, attending there 1973 to 1974.
Her professional debut was in a concert performance at London's Queen Elizabeth Hall of Donizetti's Rosmonda d'Inghilterra, in the title role. This was a nearly textbook lucky break. The soprano scheduled to sing, Janet Price, had to cancel, and Kenny was given four days to learn the part in this virtually unknown opera. This gained her excellent reviews and led to her being engaged by Covent Garden. Realizing they had obtained a special artist, Covent Garden reserved her debut at the house for a world premiere -- Hans Werner Henze's We Come to the River, in 1976. Covent Garden immediately cast her in several more roles in operas from Handel (Alcina, Semele) to Britten (Helena in A Midsummer Night's Dream), with Mozart's roles of Ila (Idomeneo), Pamina, Servilia, and Susanna, and other parts such as Sophie in Der Rosenkavalier, another Sophie in Werther, and Micaëla in Carmen. The Rosenkavalier role was also her debut part at the English National Opera in 1977. Soon she was singing in major houses around the world, including as often as she could guest performances with the Australian Opera, where she has sung Debussy's Mélisande, Massenet's Manon, Leila, Countess Adele, Fiordiligi, Alcina, and Handel's Cleopatra. She has continued to add Mozart roles to her repertory, including both Donna Anna and Dona Elvira in Don Giovanni, Giunia in Lucio Silla, and Aspasia in Mitridate, Handel's Romilda in Xerxes, and the Countess in Strauss' Capriccio. Since the turn of the century, she has continued to expand her repertoire to include roles like the Marschallin in Der Rosenkavalier, the Governess in The Turn of the Screw, Dido in Purcell's opera, Blanche in A Streetcat Named Desire, and Jocasta in Oedipus Rex. As early as her debut in Rosmonda d'Inghilterra, it was recognized that she would be a natural for roles in Italian bel canto operas, and she sings several Donizetti, Bellini, and Rossini parts. She sang the title role in the world premiere of Gavin Bryars' Medea at Lyons in 1984. Other major opera houses and companies with which she has appeared included the Aix-en-Provence Festival, the Salzburg Festival, Glyndebourne Festival Opera, Zurich and Munich Opera, Washington, D.C. Opera, Scottish Opera, and many others. Kenny is an admired and popular oratorio and concert singer. On records, she can be heard as Adelia in Ugo conte di Parigi, the title roles of Emilia di Liverpool and Mayr's Medea in Corinto, Penelope Rich in Britten's Gloriana, and several Mozart roles, as well as concert works including Handel's Messiah, Mendelssohn's Elijah, and Mahler's Fourth Symphony. She was awarded the Order of Australia in 1989, and in 2000 appeared before an international television audience of millions singing at the closing ceremonies of the Sydney Olympic Games.