McKee spent two years on a mission in Brazil for the Church of Jesus Christ of Latter-day Saints before playing at Stanford.[4][5][6] His first season with the team was 2020, in which he played in one game, completing three passes for 62 yards against the then 12th-ranked Oregon Ducks. McKee competed with Jack West for the starting job in 2021. Although West started during the season opener against the Kansas State Wildcats, McKee still attempted 18 passes, completing 15 of them for 118 yards and a touchdown.[7] He was named the starter for the following week's game against the USC Trojans.[8][9] In just his 4th collegiate start, McKee led the unranked Cardinal to a miraculous upset victory against the #3 ranked Oregon Ducks, throwing 3 touchdowns and spearheading an 87-yard game-tying drive at the end of the 4th quarter.[10]
McKee was selected by the Philadelphia Eagles in the sixth round, 188th overall, of the 2023 NFL draft.[13] He made his NFL debut in Week 17 of the 2024 season against the Dallas Cowboys in relief of Kenny Pickett. He completed three passes for 54 yards and two touchdowns in the 41–7 win.[14] McKee was named the starter for Week 18 against the New York Giants after Pickett and Jalen Hurts were declared inactive. With the #2 seed already secured; McKee threw for 269 yards and 2 touchdowns with no turnovers as the Eagles defeated the Giants 20–13, giving McKee his first NFL victory.[15]