Born in Sydney, she first studied at the University of Sydney in science, hoping to become a biochemist, but decided to pursue a career in music instead. She studied first with Myra Lambert at the Sydney Conservatorium of Music, and later won a scholarship to study at the opera school at La Scala in Milan. After a year of studying there, she went to England, where after a few recitals and TV appearances, her breakthrough came on 11 October 1975, when she replaced, with only four days' notice, the soprano scheduled to sing in an Opera Rara concert performance of Donizetti's Rosmonda d'Inghilterra at the Queen Elizabeth Hall. It was a triumph and the virtually unknown Kenny became an overnight star.
She made her debut at the Royal Opera House the following year, in the premiere of Hans Werner Henze's We Come to the River, later singing in Handel operas such as: Semele, Alcina, Giulio Cesare, and such Mozart operas as: Idomeneo, Mitridate, re di Ponto, La clemenza di Tito, The Abduction from the Seraglio, The Magic Flute. She also sang Sophie in both Werther and Der Rosenkavalier. She was also a regular guest at the Glyndebourne Festival and the English National Opera. On the international scene, she appeared at opera houses in Zurich, Munich, Vienna, Aix-en-Provence, Washington, etc. She often returned home, appearing at the Sydney Opera House in roles including: Mélisande, Manon, Leila, Micaela, Fiordiligi, Pamina, and Cleopatra. Later she sang the roles of Richard Strauss.
In 2009, Kenny appeared as Blanche DuBois in the Australian premiere of Previn's A Streetcar Named Desire for Opera Australia. After her initial success with Opera Rara, she appeared in many recordings with them, notably: Donizetti's Ugo, conte di Parigi and Emilia di Liverpool, Meyerbeer's Il crociato in Egitto, and Johann Simon Mayr's Medea in Corinto. She also provided the voice for the title role in the TV mini-series Melba, about Dame Nellie Melba.
She was made a Member of the Order of Australia (AM) in the 1989 Queen's Birthday Honour List for "services to opera", and in June 1999 was awarded an honorary Doctorate of Music by the University of Sydney.
- Simple Gifts (1993)
- Something Wonderful (1996)
- Make Believe (1998)
- A Christmas Gift (2000)
- Grove Music Online, Elizabeth Forbes, March 2008.