A successful deployment of drones provides an ideal solution for surveillance systems. Using drones for surveillance can provide access to areas that may be difficult or impossible to reach by humans or in-land vehicles gathering images or video recordings of a specific target in their coverage. Therefore, we introduces a data delivery drone to transfer collected surveillance data in harsh communication conditions. This paper proposes a Myerson auction-based asynchronous data delivery in an aerial distributed data platform in surveillance systems taking battery limitation and long flight constraints into account. In this paper, multiple delivery drones compete to offer data transfer to a single fixed-location surveillance drone. Our proposed Myerson auction-based algorithm, which uses the truthful second-price auction (SPA) as a baseline, is to maximize the seller's revenue while meeting several desirable properties, i.e., individual rationality and incentive compatibility while pursuing truthful operations. On top of these SPA-based operations, a deep learning-based framework is additionally designed for delivery performance improvements.