Aerial base station (ABS) is a promising solution for public safety as it can be deployed in coexistence with cellular networks to form a temporary communication network. However, the interference from the primary cellular network may severely degrade the performance of an ABS network. With this consideration, an adaptive dynamic interference avoidance scheme is proposed in this work for ABSs coexisting with a primary network. In the proposed scheme, the mobile ABSs can reconfigure their locations to mitigate the interference from the primary network, so as to better relay the data from the designated source(s) to destination(s). To this end, the single/multi-commodity maximum flow problems are formulated and the weighted Cheeger constant is adopted as a criterion to improve the maximum flow of the ABS network. In addition, a distributed algorithm is proposed to compute the optimal ABS moving directions. Moreover, the trade-off between the maximum flow and the shortest path trajectories is investigated and an energy-efficient approach is developed as well. Simulation results show that the proposed approach is effective in improving the maximum network flow and the energy-efficient approach can save up to 39% of the energy for the ABSs with marginal degradation in the maximum network flow.