[1] In his senior year, he struck out 20 batters in a game against Eaglecrest High School at Coors Field.

In 2018, he pitched for both Charlotte and the Montgomery Biscuits,[6] compiling a combined 9–6 record and 3.08 ERA 25 games (22 starts).

[8] In 2019, Burke was optioned to the Frisco RoughRiders of the Double-A Texas League to open the season.

[5] On August 6, Burke was promoted to the Nashville Sounds of the Triple-A Pacific Coast League.

[16] Burke missed the entire 2020 season, after undergoing surgery to repair a torn labrum in his left shoulder in February 2020.

[17] Burke spent 2021 season with the Round Rock Express of the Triple-A West, going 1–5 with a 5.68 ERA and 97 strikeouts over 77+2⁄3 innings.

On April 12, 2024, following a poor outing against the Houston Astros, he punched a wall in frustration and suffered a fractured right hand.

On multiple occasions while in the minor leagues, Burke was witnessed by different roommates waking up suddenly during the night and acting out in various ways.