An integrated energy distributed low-carbon economic dispatch model that considered multiple flexible resources was proposed, aiming at the problem of insufficient system flexibility and low carbon of integrated energy systems (IES) with multiple parks. Firstly, the flexibility requirements of the system were analyzed, the IES flexibility margin constraints were proposed, and multiple flexibility resource models including carbon capture plants were constructed to make full use of the flexible operation mode of carbon capture plants. Second, ladder-type carbon trading was introduced to establish a two-tier scheduling model for the integrated energy system. The upper layer of the model aimed to minimize the cost of energy supply by energy suppliers, and the lower layer aimed to minimize the operating cost of energy operators consisting of energy hubs (EH). The model was solved by using the objective cascade analysis method to achieve the collaborative scheduling between the upper and lower layers of the energy supplier and energy service provider with respect to the characteristics of the multi-subject operation. Finally, the positive effect of the proposed model on enhancing the system flexibility and low carbon was verified through an arithmetic example consisting of IEEE30-node network, Belgium 20-node gas network and multiple energy hubs.