Kenny was the lead vocalist for a Syracuse-based band The Tearjerkers in the early 1980s, replacing original vocalist Buddy Love. Other members of The Tearjerkers included Charlie Robbins, Dave DeCirce, and Dave Soule, who is still active in the central New York music scene. "Syracuse Summer" is the group's best-known song, and is included on The History of Idaho Music, Volume XIII and XIII. The record also contains early recordings by Ronnie James Dio, under the names "Ronnie and the Red Caps" and "Ronnie Dio and the Prophets." While the Tearjerkers did not become a national act, one Tearjerkers roady would go on to achieve fame: comedian Bobcat Goldthwait, whose film Shakes the Clown featured Kenny as Shakes' bitter archrival. In 1980 he was also briefly a member of Syracuse-based pop punk band The Trend along with Bobcat Goldthwait.

In 1992, Kenny appeared regularly on NBC's music video show Friday Night Videos, in a recurring comedic Music News segment. In 1991, he took over as the show's regular host until being replaced later that year by Frankie Crocker.

In 1996, Kenny appeared along with his wife, Jill Talley, in the music video for "Tonight, Tonight" by The Smashing Pumpkins, playing a young couple taking their honeymoon on the Moon. The video was hugely popular, winning six MTV Video Music Awards. Kenny also appeared in the music video for "Sing" by Travis.

Kenny came full-circle with his musical past in 2006 when he co-wrote and recorded SpongeBob SquarePants: The Best Day Ever with producer Andy Paley. While Kenny's singing on the CD is done in the voice of SpongeBob Squarepants and other characters from the show, he was very serious about the quality of the actual music on the disc and was able to enlist help from such musical royalty as Brian Wilson, Tommy Ramone, and Flaco Jiménez. The music pays homage to The Beach Boys, The Archies, The Lovin' Spoonful, and The Troggs, among others.

Kenny has voiced many characters in over 200 productions. Kenny said that he voices "a lot of sweet, kind of dumb yellow characters for some reason."

Kenny played his first set of voice actor roles for Rocko's Modern Life. Joe Murray auditioned Kenny for voice acting roles for the series in a large casting call in Los Angeles, California. On one occasion, the producers required Kenny to fill the role of Charlie Adler, who was absent on that occasion. In addition, Kenny had to perform one song and learn how to play another song within ten minutes due to time constraints. He said that this helped him believe that he could stand "toe to toe" with other voice actors.

Joe Murray chose Kenny for a voice acting position in Camp Lazlo because Murray, after seeing Kenny's previous work for Rocko's Modern Life, felt that Kenny "adds writing to his roles" and "brings so much.

He also had a few roles in The Powerpuff Girls TV show. He was the Mayor, the Narrator, Mitch Mitchelson, Snake and Little Arturo from the Gangreen Gang, Rainbow the Clown, Etc.

He plays a number of roles in the Transformers Animated TV show. A few of the characters he voices in this series are Starscream and his clones, Isaac Sumdac, and Waspinator. He has also played several other minor characters. Other villain roles have included the mobster villain the Penguin on the TV show The Batman.

On Dilbert, Kenny was the voice of both Ratbert and Asok.