He played college football for the Texas A&M Aggies, and was selected by the Arizona Cardinals in the second round of the 2018 NFL draft.

[3][4] Sources: Kirk attended and played college football at Texas A&M under head coach Kevin Sumlin.

[13] In the Cardinals' season-opening loss to the Washington Redskins, Kirk had a four-yard reception to go along with two punt returns for 44 net yards in his NFL debut.

[15] In Week 5 against the San Francisco 49ers, he caught a 75-yard touchdown bomb from fellow rookie Josh Rosen to help the Cardinals earn their first win of the season by a score of 28–18.

[19] In Week 2 against the Baltimore Ravens in 2019, Kirk caught six passes for 114 yards as the Cardinals lost 23–17.

[20] In Week 10 against the Tampa Bay Buccaneers, Kirk caught 6 passes for 138 yards and three touchdowns in the 30–27 loss.

[41] On November 2, after suffering a season-ending broken collarbone in a Week 8 matchup against the Green Bay Packers, Kirk was placed on injured reserve.

[42] On March 6, 2025, a trade that would send Kirk to the Houston Texans for a seventh-round pick in the 2025 NFL draft was agreed in principle.

[43] On May 14, 2018, it was revealed that Kirk was arrested for disorderly conduct and causing property damage in Scottsdale, Arizona, which occurred on February 3, more than two months prior to the draft.

Kirk allegedly threw rocks at cars while attending the Waste Management Phoenix Open at TPC Scottsdale.