Accurate mapping of greenhouse gas fluxes at the Earth's surface is essential for the validation and calibration of climate models. In this study, we present a framework for surface flux estimation with drones. Our approach uses data assimilation (DA) to infer fluxes from drone-based observations, and reinforcement learning (RL) to optimize the drone's sampling strategy. Herein, we demonstrate that a RL-trained drone can quantify a CO2 hotspot more accurately than a drone sampling along a predefined flight path that traverses the emission plume. We find that information-based reward functions can match the performance of an error-based reward function that quantifies the difference between the estimated surface flux and the true value. Reward functions based on information gain and information entropy can motivate actions that increase the drone's confidence in its updated belief, without requiring knowledge of the true surface flux. These findings provide valuable insights for further development of the framework for the mapping of more complex surface flux fields.