Blythe began his career with small supporting roles in the 2010 films Robin Hood and Blood of the Pelican. In 2018, he starred opposite Richard Mason in the coming-of-age film Scott & Sid. After graduating from Juilliard, Blythe was cast as Glen Byam Shaw in Terence Davies' biographical drama film Blessing, which premiered the following year.

In 2022, Blythe had a guest role on The Gilded Age and began playing the series' title character Billy the Kid. Blyth played the title character Coriolanus Snow in the 2023 film The Hunger Games: The Ballad of Serpents and Songbirds, an adaptation of the Hunger Games prequel of the same name. He has roles ahead of him in the comedy Discussion Papers, adapted from Bill Keenan's memoirs, as well as in the new adaptation of Ernest Hemingway's novel A Farewell to Arms!