Kenney started in New Jersey band called Racecar in 1994 with Jimmie Muller and Sam Hofman. After this, he and Chuck Treece started a musical duo called Supergrub in 1996, with three CDs released: Norma & Thurselle, Communicator and Challenger.

Kenney played guitar for the hip-hop group The Roots before he joined Incubus in 2003 after the departure of the bass guitarist and founding member Alex Katunich (aka Dirk Lance). He had previously played with Incubus members Mike Einziger and Jose Pasillas in Time Lapse Consortium.

He has five solo albums, 26 released on December 1, 2004, Maduro released on March 1, 2006, Distance and Comfort released on January 15, 2008, Burn The Tapes released on October 1, 2010, and Leave On Your Makeup released on September 17, 2013. Kenney plays guitar, bass guitar and drums while singing and writing every part on the solo records. When touring to support his solo records he plays guitar and sings, accompanied by Ashley Mendel on bass guitar and vocals and Sekou Lumumba on drums. Recently, Simon Harding from the band Fin has replaced Lumumba.

His bass equipment includes Lakland bass guitars, Line 6 effects “(interview)”. Archived from the original on February 3, 2009. Retrieved January 26, 2008. and Mesa Boogie amplifiers. His collection of bass guitars includes a seafoam-green USA Joe Osborn, sunburst USA Joe Osborn with a fretless fingerboard, sunburst Skyline Joe Osborn, red Skyline Bob Glaub, shoreline gold Skyline Hollowbody, custom 44-94, light blue 44-94, cherry sunburst 55-94 with Gibson knobs, fiesta red 30″ Jazz Bass (44-60), 1975 Fender Jazz Bass, Gibson SG Bass, Fender Jaguar Bass, and a Hofner 500/1 “Beatle Bass”. Most of his bass guitars have rosewood fingerboards and are strung with GHS flatwounds, with the exception of the Skyline Bob Glaub and the 55-94 which are strung with Thomastik-Infeld roundwounds. Kenney also plays Gibson Les Pauls which is seen in the DVD video for “Not Today”. His live Mesa/Boogie rig consists of a pair of Big Block 750 heads and a Roadready 8×10 cabinet. In the studio and for solo gigs and small live gigs with Incubus, he uses Mesa Walkabout 1×12 combos and extension cabs.