The objective of this study is to characterize the performance of a passive TE flap in the load mitigation of an airfoil at low-Reynolds numbers. Specifically, we aim to evaluate when non-linear effects (boundary layer separation and/or leading-edge vortex formation) become relevant for the load-mitigation capability of the passive flap, and how can these effects be taken into account in the preliminary design of passive flaps for low-Re applications. To that end, we perform direct numerical simulations of the 2D incompressible flow around airfoils incorporating passive-pitching trailing edge flaps at Re=1000. The time-varying effective angle of attack of the airfoil, defined as the angle between the relative velocity experienced by the airfoil and its mean chord line, is induced by imposing a vertical (heaving) motion of the airfoil. The analysis is performed for a wide range of kinematics (i.e., reduced frequencies and heaving amplitudes) and flap lengths. This dataset contains videos showing the time evolution of the instantaneous vorticity field around the airfoil, for a number of selected cases. Each case is characterized by the length of the flap (a), the frequency of the heaving motion of the airfoil (f), the heaving amplitude (h), the density of the flap (rho_s) and the mean geometric angle of attack of the airfoil (alpha). Variables are normalized with the free-stream velocity (U_inf), the airfoil chord (c), and the fluid density (rho). Case A1 corresponds to rho_s/rho = 1.5, pi*f*c/U_inf = 0.3, h/c = 0.15. Values of a/c = [0, 0.25, 0.375, 0.5, 0.75] and alpha=[0, 5º] are considered. Case A2 corresponds to rho_s/rho = 1.5, pi*f*c/U_inf = 0.3, h/c = 0.25. Values of a/c = [0, 0.25, 0.375, 0.5, 0.75] and alpha=[0, 5º] are considered. Case A3 corresponds to rho_s/rho = 1.5, pi*f*c/U_inf = 0.3, h/c = 0.50. Values of a/c = [0, 0.25, 0.375, 0.5, 0.75] and alpha=[0, 5º] are considered. Case B1 corresponds to rho_s/rho = 1.5, pi*f*c/U_inf = 0.5, h/c = 0.15. Values of a/c = [0, 0.25, 0.375, 0.5, 0.75] and alpha=[0, 5º] are considered. Case B2 corresponds to rho_s/rho = 1.5, pi*f*c/U_inf = 0.5, h/c = 0.25. Values of a/c = [0, 0.25, 0.375, 0.5, 0.75] and alpha=[0, 5º] are considered. Case B3 corresponds to rho_s/rho = 1.5, pi*f*c/U_inf = 0.5, h/c = 0.50. Values of a/c = [0, 0.25, 0.375, 0.5, 0.75] and alpha=[0, 5º] are considered.