Burney started his youth career with local side Blue Arrows before joining Seattle United in 2010.[1] He joined the Seattle Sounders FC academy in 2015.[2] He made his debut for USL club Seattle Sounders FC 2 in August 2018.[3]
In the summer of 2022, Burney joined the inaugural roster for USL League Two club Ballard FC. He rejoined the team for the 2023 season.[4]