The unmanned aerial vehicle (UAV) based multi-access edge computing (MEC) appears as a popular paradigm to reduce task processing latency. However, the secure offloading is an important issue when occurring aerial eavesdropping. Besides, the potential uncertainties in practical applications and flexible trajectory optimizations of UAVs pose formidable challenges for realizing robust offloading. In this paper, we consider the aerial secure MEC network including ground users, service unmanned aerial vehicles (S-UAVs) integrated with edge servers, and malicious UAVs overhearing transmission links. To deal with the task computation complexities, which are characterized as uncertainties, a robust problem is formulated with chance constraints. The energy cost is minimized by optimizing the connections, trajectories of S-UAVs and offloading ratios. Then, the proposed non-linear problem is tackled via the distributionally robust optimization and conditional value-at-risk mechanism, which is further transformed into the second order cone programming forms. Moreover, we decouple the reformulated problem and design the successive convex approximation for S-UAV trajectories. The global algorithm is designed to solve the sub-problems in a block coordinate decent manner. Finally, extensive simulations and numerical analyses are conducted to verify the robustness of the proposed algorithms, with just 2\% more energy cost compared with the ideal circumstance.