Kennedy was born in Manchester, England, around 1855 (obituaries stated his age as either 39 or 45, the latter putting his birth year around 1849), and was a talented ventriloquist as a child.
After working briefly as a teacher and seaman, by 1871 he had made it to Montreal and began performing as a ventriloquist.
In 1890, he opened "Harry Kennedy's Theatre" in New York, but sold out and moved after one season to a smaller venue, the Alhambra, on Coney Island.
Songs he wrote include "When Peggy And I Are Wed", "Molly and I and the Baby", "Say Au Revoir, But Not Good-bye", "A Flower from Mother's Grave", "Cradle's Empty, Baby's Gone", "An Old Fashioned Photograph", "Patsy Branigan", "I Owe Ten Dollars to O'Grady", "I Had Fifteen Dollars in my Inside Pocket", "Hush Don't Wake the Baby", "Grandmother's Birthday" and "Little Empty Stockings By the Fire".
He married again in 1886 and his second spouse (Mary, sister of Nellie Brock) died in 1890.