Burleson's first assignment was in the 7th Infantry Division (Light), Fort Ord, California, which included service in the Multi-National Force and Observers, Sinai Peninsula, Egypt, and the invasion of Panama.

He later commanded airborne companies in Vicenza, Italy, which included service as part of the initial entry force for operations in Bosnia-Herzegovina.

Burleson later served in the 82nd Airborne Division at Fort Bragg, North Carolina, with deployments to Kosovo and Afghanistan.

After attending the United States Army War College, Burleson returned to the 10th Mountain Division as commander of the 1st Brigade, which included a deployment to Regional Command-North, Afghanistan.

Burleson later served as the Deputy Commanding General (Operations), 7th Infantry Division (United States), Joint Base Lewis-McChord, Washington, and Director of the Mission Command Center of Excellence at Fort Leavenworth, Kansas, and as senior advisor to the Ministry of Defense, Afghanistan.