The dispersion of plant pathogens, such as rust spores, is responsible for more than 20% of global crop yield loss annually. However, the release mechanism of pathogens from flexible plant surfaces into the canopy is not well understood. In this study, we investigated the interplay between leaf elasticity and rainfall, revealing how a flexible leaf structure can generate a lateral flow stream, with embedded coherent structures that enhance transport. We first modeled the linear coupling between drop momentum, leaf vibration, and the stream flux from leaf surfaces. With Lagrangian diagnostics, we further mapped out the nested coherent structures around the fluttering profile, providing a dynamical description for local spore delivery. We hope the mechanistic details extracted here can facilitate the construction of physically informed analytical models for local crop disease management.