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Federated learning (FL) represents a promising distributed machine learning paradigm that allows smart devices to collaboratively train a shared model via providing local data sets. However, problems considering multiple co-existing FL services and different types of service providers are rarely studied. In this paper, we investigate a multiple FL service trading problem in Unmanned Aerial Vehicle (UAV)-aided networks, where FL service demanders (FLSDs) aim to purchase various data sets from feasible clients (smart devices, e.g., smartphones, smart vehicles), and model aggregation services from UAVs, to fulfill their requirements. An auction-based trading market is established to facilitate the trading among three parties, i.e., FLSDs acting as buyers, distributed located client groups acting as data-sellers, and UAVs acting as UAV-sellers. The proposed auction is formalized as a 0-1 integer programming problem, aiming to maximize the overall buyers' revenue via investigating winner determination and payment rule design. Specifically, since two seller types (data-sellers and UAV-sellers) are considered, an interesting idea integrating seller pair and joint bid is introduced, which turns diverse sellers into virtual seller pairs. Vickrey-Clarke-Groves (VCG)-based, and one-sided matching-based mechanisms are proposed, respectively, where the former achieves the optimal solutions, which, however, is computationally intractable. While the latter can obtain suboptimal solutions that approach to the optimal ones, with low computational complexity, especially upon considering a large number of participants. Significant properties such as truthfulness and individual rationality are comprehensively analyzed for both mechanisms. Extensive experimental results verify the properties and demonstrate that our proposed mechanisms outperform representative methods significantly.