With the increasing integration of distributed energy and flexible resources, efficient coordination and trading mechanisms are urgently required in integrated energy distribution systems. This paper proposes a trading strategy based on a non-cooperative game-theoretic framework to model the multi-agent interactions among distribution network, integrated energy systems (IES), and distributed flexible resources. In the upper-level model, a dynamic game is formulated between the power grid and IESs, where the IESs incorporate distributionally robust chance constraints to handle renewable energy uncertainty. Distribution locational marginal price (DLMP) signals are generated as the outcome of this game. In the lower-level model, flexible resources adjust their energy demand in response to DLMP signals, thereby influencing price formation through demand-side decisions. A fixed-point iteration algorithm is employed to coordinate the bi-level model, and the alternating direction method of multipliers (ADMM) is used to solve the upper-level game in a distributed manner. Simulation results demonstrate that the proposed strategy effectively coordinates multi-agent behaviors, enhances system flexibility, and promotes the active participation of flexible resources in distribution-level market operations.