Thin non-uniform particle size wicks are essential to improve the maximum heat flux of two-phase thermal management systems by improving the wickability. To understand the enhanced wickability, we examine a pore-scale capillary flow within the thin sintered particle wick using a free-energy-based, single-component, two-phase Lattice Boltzmann Method (LBM) with a minimal parasitic current. The developed LBM approach is validated through the rate-of-rise in the two-parallel plates with parallel plates spacing of W = 48 against analytical Bosanquet equation, achieving the RMS error below 10%. The LBM predicts the rate-of-rise through the uniform and non-uniform particle-size wicks between two-parallel plate, including the capillary meniscus front and dynamic capillary filling. At the same plate spacing and porosity, i.e., W = 48 lu and ε = 0.75, the non-uniform particle size wick achieves enhanced wickability by providing the selective flow pathway through pore networks formed in the smaller pores between the small/large particles, which is in qualitative agreement with previous experimental results. The enhancement of the maximum and minimum dimensionless liquid height and the liquid-filled pore ratio of non-uniform particle size wick is found to be up to 11.1, 27.47, and 26.11%, respectively. The simulation results provide insights into the optimal wick structures for high heat flux two-phase thermal management system by enhancing the wickability through the non-uniform particle (or pore) sizes.