McKenzie recently starred in the ABC docudrama miniseries When We Rise, helmed by Dustin Lance Black and Gus Van Sant. He portrays the young LGBT Activist Cleve Jones in the period piece, which chronicles the personal and political struggles, setbacks and triumphs of a diverse family of LGBTQ people who helped pioneer an offshoot of the Civil Rights Movement from its turbulent infancy in the 20th century to the once unfathomable successes of today. When We Rise tells the history of the modern gay rights movement, starting with the Stonewall riots in 1969. McKenzie also sings "Thinking of You" from the When We Rise Soundtrack.

Soon after graduating from Columbia College Chicago, McKenzie sent in a tape to Director Michael Arden and the creative team at Deaf West Theatre, with hopes of obtaining a job as an interpreter during the company's ASL-inclusive run of Spring Awakening. However, the Deaf West team saw his potential, and requested he audition for the leading role in the production—the radical atheist Melchior Gabor. He was given the role, and began rehearsing for the show in mid-2014. At first, McKenzie was the only member of the hearing cast that was able to effectively communicate with their deaf and hard-of-hearing cohorts, thanks to his training in ASL. Deaf West's Spring Awakening originally performed at a 99-seat theatre off of skid row in Los Angeles, California from September 14, 2014 to November 9, 2014. It was McKenzie's professional theatre debut.

In addition to theatre, McKenzie has appeared on both the big and small screen. In 2015, he appeared in a one-episode guest starring role in the television series The 101.

He starred in the feature film Speech & Debate, adapted from the hit 2007 off-Broadway play of the same name by Tony-winning Playwright Stephen Karam and released by Sycamore Pictures and Vertical Entertainment in select theaters and VOD on April 7, 2017. McKenzie stars as one of three leads as the character of Howie, an openly gay teenager alongside Sarah Steele, who also starred in the original off-Broadway premiere of Speech & Debate and Liam James. The film features three misfit students in high school who are frustrated with the hypocrisy they see in their parents and school staff. Together, they try to revive an extinct school debate club to face the situation in which they find themselves. A number of theater names including Darren Criss and Lin-Manuel Miranda cameo in the film and Kristin Chenoweth sings an original song for the film.