He began his career as an illustrator of children's books and a cartoonist, and expanded into animation, as well as painting, manga, sculptures, writing, and shell painting.
Kuri began the "Animation Sannin no Kai" (Animation Group of Three) in 1960 with Ryôhei Yanagihara and Hiroshi Manabe'. This was a collective that kick-started the trend of modern, independently made and adult-aimed animation in early 1960s Japan. They began hosting animation festivals in 1960, and these festivals have continued on since (not regularly, but frequently enough).
He cites avante-garde animator Norman McLaren as an influence on his work.
As of 2014 he is teaching animation at Laputa Art Animation School.
In 1996 he was awarded a Blue Ribbon and a Purple Ribbon by the Prime Minister, a Japanese lifetime achievement award.