As the most potential carbon capture technology for coal-fired power plants, oxy-fuel combustion provides a new solution for improving the flexibility of the integrated energy system and reducing carbon emissions. Based on integrating oxy-fuel combustion technology and the optimal operation of the integrated energy system, a two-stage optimal dispatch strategy for the integrated energy system with oxy-fuel combustion units considering the constraints of multi-energy flexibility is proposed. Firstly, the model of integrated energy system with oxy-fuel combustion (Oxy-IES) is established. The matrix model of multi-energy flexibility constraints for Oxy-IES is proposed, to reveal the supply and demand relationship of Oxy-IES flexibility. The two-stage optimization dispatch strategy for Oxy-IES is constructed, in which the output of each equipment is optimized with the lowest daily operating cost of carbon trading in the day ahead stage, and the rapid variable load capacity of the oxy-fuel combustion unit can improve the flexibility of the system in the intraday stage. The simulation results of Oxy-IES show that the proposed strategy can improve the flexibility and economy of IES and reduce carbon emissions.