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Turbulent mixing is a physical process of fundamental importance in high-speed premixed flames. This mixing results in enhanced transport of temperature and chemical scalars, leading to potentially large changes in flame structure and dynamics. To understand turbulent mixing in non-reacting flows, a number of classical theories have been proposed to describe the scaling and statistics of dispersing fluid particle pairs, including predictions of the effective, or turbulent, eddy diffusivity. Here we examine the validity of these classical theories through the study of fluid particle pair dispersion and eddy diffusivity in highly turbulent premixed methane-air flames at a Karlovitz number of approximately 140. Using data from a direct numerical simulation and a higher-order Lagrangian tracking algorithm, particle pair centroids are seeded at different initial temperatures and separations, and then integrated forward in time. We show that scaling relations and results developed for pair dispersion in non-reacting flows remain relevant in this high-intensity premixed flame, and we identify the impacts of heat release on dispersion and eddy diffusivity.