McKenzie's first two years with the Georgia Bulldogs only saw him accumulate 190 receiving yards and 195 rushing yards, as he was primarily used as a kick returner. After Kirby Smart replaced Mark Richt as head coach, McKenzie was more prominently featured in the Georgia passing game. He caught 44 receptions for 633 yards and 7 touchdowns as a junior, becoming the Bulldogs' top receiver. Leading into the 2017 NFL Draft, draft analyst Mel Kiper Jr. compared McKenzie to Antonio Brown due to similarities in their kick-return abilities and athleticism.
Professional career
Denver Broncos
McKenzie was drafted by the Denver Broncos in the fifth round, 172nd overall, in the 2017 NFL Draft. On September 11, 2017, in the season opener against the Los Angeles Chargers on Monday Night Football, McKenzie returned three punt returns for 48 net yards in his NFL debut. On September 24, against the Buffalo Bills, McKenzie recorded his first career rushing attempt, a four-yard carry. He totaled four receptions for 29 yards on the season. On September 10, 2018, McKenzie was waived by the Broncos and was re-signed to the practice squad. He was promoted to the active roster on October 25, 2018. He was waived again on November 2, 2018.
Buffalo Bills
On November 5, 2018, McKenzie was claimed off waivers by the Buffalo Bills.
2018
McKenzie was used as the primary kick returner, but also saw significant time on offense. He scored his first NFL touchdown, rushing 6 yards on a jet sweep, against the Jacksonville Jaguars on November 25. Against the New York Jets, he was used in the run game after LeSean McCoy and Chris Ivory suffered injuries, rushing for 22 yards on four carries with another touchdown to go with 47 receiving yards in the 27–23 loss. He had 18 receptions for 179 receiving yards to go along with 66 rushing yards and two rushing touchdowns on the season.
2019
McKenzie's kick return role decreased after the Bills added free agent kick returner Andre Roberts, but he still found decent playing time on special teams and as a gadget player on offense. He caught 27 passes for 254 yards and a touchdown, in addition to rushing 8 times for 49 yards. McKenzie played a big role in helping the Bills defeat the Tennessee Titans in week 5, as his 46-yard reception helped set up the game-winning touchdown. For the Bills' final game of the 2019 season, against the Jets, he was pressed into service as a reserve cornerback, as the Bills were resting the starters and the backups suffered injuries.
2020
On March 30, 2020, McKenzie re-signed with the Bills.
