In this work, we study data collection in multiple unmanned aerial vehicle (UAV)-aided mobile wireless sensor networks (WSNs). The network topology is changing due to the mobility of the UAVs and the sensor nodes, so the design of efficient data collection protocols is a major concern. We address such high dynamic network and propose two mechanisms: prioritized-based contact-duration frame selection mechanism (PCdFS), and prioritized-based multiple contact-duration frame selection mechanisms (PMCdFS) to build collision-free scheduling and balance the nodes between the multi-UAV respectively. Based on the two mechanisms, we proposed a Balance algorithm to conduct the collision-free communication between the mobile nodes and the multi-UAVs. Two key design ideas for a Balance algorithm are: (a) no need of higher priority for those nodes that have lower transmission rate between them and the UAV and (b) improve the communication opportunity for those nodes that have shorter contact duration with the UAVs. We demonstrate the performance of proposed algorithms through extensive simulations, and real experiments. These experiments using 15 mobile nodes at a path with 10 intersections and 1 island, present that network fairness is efficiently enhanced. We also confirm the applicability of proposed algorithms in a challenging and realistic scenario through numerous experiments on a path at Tongji campus in Shanghai, China.