Island microgrids adjacent to each other form an island microgrid cluster, which can realize optimal resource allocation among microgrids with different source-load characteristics through energy sharing, thereby improving economic performance, reliability and renewable energy utilization of regional power system operation. To solve the energy management problem, a hierarchical energy management architecture of the island microgrid cluster is established based on a multi-agent system. On this basis, the risk of flexibility shortage index is introduced to evaluate the impact of renewable energy output uncertainty on system operation. A multi-objective optimization energy management strategy and a cluster layer energy allocation strategy are constructed. The linearized model is solved by the tolerant lexicographic method. Finally, an island microgrid cluster consisting of four microgrids is taken as an example to verify the effectiveness of the proposed energy management strategy. This work is supported by Science and Technology Project of State Grid Corporation of China (No. 52170018000S).