The goal of this work is to study via molecular simulations the wetting kinetics of a rough surface by an oily fluid. We use forward flux sampling to compute the wetting transition rate and elucidate the transition mechanism of a small droplet on a surface of nails. The nails provide the re-entrant geometry necessary to keep the droplet in the nonwetted, composite state. The effects of nail height, droplet size, and surface chemistry are investigated. Because the droplet must touch the bottom surface to transition, increasing the nail height is an effective way to increase the barrier to wetting for both phobic and slightly philic drops, although as the fluid becomes very philic, chemistry dominates and the effect of nail height disappears. Generally, smaller drops transition more easily. Overall, our results suggest that nonwettability could be practically enhanced by promoting the "kinetic" trapping of the system in the nonwetted state.