Studies of swimming animals contribute to recent and future developments of efficient propulsion for autonomous underwater vehicles but mostly focus on flapping foils at low Reynolds numbers (Re). Flapping foils for large-size underwater vehicles can experience from intermediate to high Re at which the ratio of inertia to viscous effect is important. In this work, we study a NACA0016 foil undergoing propulsive heave and pitch motions using 3-D simulations of wall-resolved LES and an Immersed Boundary Method. We characterize the instantaneous vorticities and phase-averaged flow fields, especially the near-wall parameters for both velocity and pressure. Similar to \(Re=10,000\) , we found that flapping foils at \(Re=1,000,000\) and a Strouhal number of \(St=0.3\) experience cyclic behaviours. Flapping foils at higher Re can still experience laminar flow mostly at the pressure side, depending on the phases and locations, but turbulent on the suction side. Their near-wall flow characteristics show dynamic pressure gradients and advection speeds dictated by the kinematics and Re. We found that vortex breakdown coincides with the advection path. The inner layer advection at high Re can be faster than the outer edge of the boundary layer due to the advection of smaller vortices. At lower Re, the advection speed is related to a large LEV and is similar for inner and outer-edge boundary layers.