Si3N4-based ReRAM devices showcase intriguing performance characteristics of low switching threshold, high endurance and retention that lay the foundations for the development of the next-generation low-power artificial synaptic devices. In this work, an approach to accurately simulate resistive-switching of Si3N4 memristors by employing the Kinetic Monte Carlo simulation method is outlined. The Kinetic Monte Carlo (KMC) method is used to simulate the temporal dynamics of the conductive filament (CF) formation and recession during voltage sweeps on the devices under simulation. The CF is modeled as nitrogen vacancies which act as electron transfer sites, consistent with experimental data showing conductivity in Si3N4 films having high nitrogen vacancy concentrations. This simulation approach allows for direct visualization of the CF electrostatics as well as the incorporation of a non-local, trap-assisted tunneling model to approximate current-voltage characteristics during the switching event.