Flying base stations (FlyBSs) enable ubiquitous communications in the next generation mobile networks with a flexible topology. However, a deployment of the FlyBSs intensifies interference, which can result in a degradation in the throughput of cell-edge users. In this paper, we introduce a flexible soft frequency reuse (F-SFR) that enables a self-organization of a common SFR in the networks with an unpredictable and dynamic topology with the FlyBSs. We propose a graph theory-based algorithm for an allocation of resource plans, which is understood as a bandwidth allocation and a transmission power setting in the context of SFR. Furthermore, we introduce a low-complexity implementation of the proposed resource allocation using deep neural network (DNN) to significantly reduce the computation complexity. We show that the proposed F-SFR increases the throughput of cell-edge users by 16% to 26% and, at the same time, improves the satisfaction of the cell-edge users by up to 25% compared to the state-of-the-art solutions. We also demonstrate that the proposed scheme ensures a higher fairness in the throughput among the users with respect to the state-of-the-art solutions. The implementation via DNN also outperforms all state-of-the-art solutions despite its very low complexity.