Baker, at 3 feet, 8 inches (112 cm) tall, was a circus and cabaret performer with entertainer Jack Purvis when George Lucas hired him to be the man inside R2-D2 in Star Wars in 1977. Though both he and his wife have dwarfism, their two sons do not. Baker appears in five of the six Star Wars films; though credited on Episode III, he never filmed any scenes. George Lucas decided to credit him in the film out of loyalty. Baker even played an additional role in 1983's Return of the Jedi as Paploo, the Ewok who stole an Imperial speeder bike. He was originally going to play Wicket W. Warrick, but he fell ill, and that role was handed over to Warwick Davis.
Baker has also worked with George Lucas outside of the Star Wars films. Baker had an uncredited role as R2-D2 in Star Tours and an uncredited role as a Nelwyn band member in Willow, as well as a role as the Goblin Corps in Labyrinth.
Baker's other films include 1980's The Elephant Man, 1981's Time Bandits, 1984's and the 1986 Jim Henson film Labyrinth. In the late 1990s, Baker launched a stand up comedy career. Kenny is a first class mouth-organ player and rates his guest appearance with the James Coutts Scottish Dance Band at Hugh McCaig's Silverstone Party in July 1997 as probably his "finest musical experience."