Burke began his collegiate soccer career at Eastern Illinois University, playing from 2016 to 2021. Over the course of his five seasons, he made a total of 56 appearances and recorded 254 saves. Throughout his college career, Burke was recognized for his impressive skills, earning the title of Defensive Player of the Week twice in 2018. In addition, his strong performances earned him his first All-Conference second-team award in 2019.
In his graduate year, Burke transferred to Drake University to further his development on the field. During the 2022 season, he played in 15 games, earning 62 saves and five clean sheets. His stellar performances throughout the season helped him earn the 2022 MVC Goalkeeper of the Year award.
After completing his college career, Burke made the leap to professional soccer. Burke was signed to MLS Next Pro team Chattanooga FC, for the 2023 and 2024 season where he made 13 appearances.