Leslie began work for NASA in 1980 as a research scientist in the Space Science Laboratory at the Marshall Space Flight Center. Since 1983, he has served as a co-investigator for the Geophysical Fluid Flow Cell experiment which examines spherical rotating convection relevant to the atmospheres of stars and planets. The experiment flew on Spacelab 3 and is also a part of the United States Microgravity Laboratory-2 (USML-2) payload. Leslie was a principal investigator for the Fluid Interface and Bubble Experiment examining the behavior of a rotating free surface aboard NASA's KC-135 aircraft flying low-gravity trajectories. He is an author on 27 journal papers, 45 conference papers, and 9 NASA reports involving atmospheric and fluid dynamic phenomena. Leslie also worked in the MSFC Neutral Buoyancy Simulator as a suited subject and safety diver supporting procedure tests for extra-vehicular activity.
In 1987, he became chief of the Fluid Dynamics Branch where he directed and conducted research in both laboratory and theoretical investigations along with more than a dozen scientists in the Branch. He was also the mission scientist for Spacelab J (STS-47) coordinating more than 40 domestic and Japanese experiments in fluid dynamics, crystal growth, and life science during the 8-day mission.