We consider a class of last mile distribution problems with multicenters and multiareas in disaster management, where the travel time for every pair of center‐area is uncertain. We propose a chance‐constrained model to handle this problem, which simultaneously determines the selection of emergency logistics centers (ELCs), the amount of relief transported to these ELCs, the allocation and routing of vehicles, and the equitable distribution of emergency materials from the ELCs to the disaster areas. We develop a distributionally robust optimization (DRO) model to reformulate the chance‐constraint model as a second‐order cone programming, which the proposed algorithm can solve efficiently. We present a case study of the Yushu earthquake in the Qinghai Province of the People's Republic of China to demonstrate the performance of our proposed model and method. The results reveal that (1) the DRO method outperforms the scenario‐based model in reducing cost and improving reliability, (2) deploying a large number of vehicles in the emergency centers near disaster areas can reduce cost, and (3) our proposed model evenly distributes vehicles on paths to curtail the rescue time.