As the penetration of renewable energy increases, its uncertainty poses great challenges to the economics and robustness of integrated energy systems. To promote renewable energy consumption and reduce carbon emissions, a data-driven distributionally robust optimization (DRO) scheduling strategy is proposed. First, a flexible supply and demand response model consisting of an organic Rankine cycle (ORC), hydrogen fuel cell and electric vehicle is constructed, and a stepped carbon trading mechanism is introduced to constrain the carbon emissions of the system. Secondly, in order to obtain the probability distribution of the scene in the worst case, a comprehensive norm is used to constrain the probability distribution confidence set of the wind power output scene. Then, a two-stage robust optimization model is established with the goal of minimizing the total cost of integrated energy system (IES) operation in the worst scenario probability distribution, and the model is iteratively analyzed by a column and constraint generation (CCG) algorithm. Finally, the simulation results show the effectiveness of the proposed model and solution method. It also analyzes the influence of the ladder carbon trading mechanism and the supply and demand flexible response model in improving the system flexibility and low-carbon economy.