He began his career as a staff announcer in radio; Kennedy's voice narrates the opening of the television series Adventures of Superman.

He played Thierache, the Executioner, who sets fire to Joan (played by Ingrid Bergman) in Joan of Arc (1948), but recounted that after the picture previewed in a neighborhood popular with gays, his one line – "We need more fagots" (a term referring to a bundle of sticks used to burn someone at the stake) – generated loud laughter from the audience during the execution scene.

[2] Kennedy also appeared as a guest star in numerous series, such as The Lone Ranger, The Cisco Kid, The Gene Autry Show, and Death Valley Days.

He expressed his opinion of the movies, making comments such as "We have a moderately good picture for you today".

When Kennedy showed a film in which he had a part, he would talk at every break about the role, but always with a wink and good humor.