Having played youth football with VFC Plauen, Kühn joined Dynamo Dresden's youth team in 2018.[3][4] In December 2020, he signed a professional contract with the club, active from summer 2021.[4] He made his debut for the club as a substitute in a 3–0 3. Liga defeat at home to Hallescher FC on 24 April 2021.[1] In August 2021, he joined Sonnenhof Großaspach on loan for the 2021–22 season.[5]