The growing penetration of renewable energy needs a large amount of flexible resource to regulate in power systems. Current research mainly focuses on individual flexibility of resources, the synergistic flexible potential of thermal units with multi-energy storage systems remains underexplored. Therefore, this paper proposes a distributionally robust optimal dispatch method for multiple flexible resources including thermal units and multiple energy storage. Firstly, a refined operation model of units and energy storage is constructed. Specifically, oxygen-enriched deep peaking of units and coordinated operation of battery and hydrogen energy storage are considered. Secondly, a data-driven distributionally robust optimization (DRO) model is established to cope with the uncertainties of renewable energy. An inexact columns and constraint generation (i-C&CG) method is then developed to solve the model efficiently. Finally, a case study of a provincial power system is conducted, and the results verify the validity of the proposed method.