Kazee accepted a football scholarship from San Diego State, following in the footsteps of his older brother Walter, who was a running back with the Aztecs.

He made 41 tackles (3 for loss), one interception, 2 pass breakups, one sack, 4 forced fumbles (tied for fourth in school history) and one blocked kick.

As a sophomore, he started all 13 games at cornerback, posting 58 tackles (4 for loss), one 13 pass breakups (led the team), one fumble recovery and 2 quarterback hurries.

[2] On January 28, 2017, he appeared in the Senior Bowl and helped Cleveland Browns head coach Hue Jackson's South team defeat the North 16–15.

On March 23, 2017, he attended San Diego State's Pro Day, but opted to stand on his combine numbers and performed positional drills, the short shuttle, and three-cone drills for scouts and team representatives from 29 NFL teams that attended, including Los Angeles Chargers defensive coordinator Gus Bradley.

[5] At the conclusion of the pre-draft process, Kazee was projected to be a fourth or fifth round pick by the majority of NFL draft experts and scouts.

[9] Kazee entered training camp competing against Brian Poole for the starting nickel back role.

Head coach Dan Quinn opted to transition him to free safety in July and Kazee showed promise throughout training camp in his new role.

On October 1, 2017, Kazee earned his first career start after Ricardo Allen was unable to play after suffering a concussion the previous week.

Kazee ended the 2018 season third on the team with 82 combined tackles, and tied for the league lead with seven interceptions with Kyle Fuller and Xavien Howard.

[14] In Week 11 against the Carolina Panthers, Kazee recorded his first interception of the season off a pass thrown by Kyle Allen in the 29–3 win.

[15] In Week 14 against the Panthers, Kazee forced a fumble on wide receiver Greg Dortch during a kickoff return which was recovered by kicker Younghoe Koo and recorded 2 more interceptions off passes thrown by Kyle Allen during the 40–20 win.

On March 29, 2021, Kazee signed as a free agent with the Dallas Cowboys, reuniting with defensive coordinator Dan Quinn, who was his head coach with the Falcons.

He appeared in 9 games with 4 starts (two due to injury and two in the three-safety package), while registering 19 tackles, 2 interceptions and 2 passes defensed.

[26] On October 19, 2021, Kazee was arrested and charged with driving while under the influence after he was pulled over for a traffic violation in The Colony, Texas.