The distributed economic dispatch of integrated energy systems is increasingly dependent on communication networks, making its information security vulnerable to severe cyber threats. Existing research is mostly limited to the defender's perspective, and lacks priori understanding of stealthy economic attacks, making proactive defense difficult to achieve. To address this issue, this paper proposes an optimal coordinated attack strategy for energy storage systems and loads from the attacker's perspective, aiming to identify the security boundary of the system and promote defense through attack analysis. First, an economic dispatch model for an electricity-heat-gas integrated energy system is constructed, and a fully distributed solution algorithm is designed. Subsequently, a three-stage coordinated attack framework is designed by taking advantage of the protection weakness of energy storage systems and loads. By combining stealthy data integrity attacks in the first two stages with a timely introduced denial-of-service (DoS) attack in the third stage, the system is forced to converge to a feasible operation point with significant economic deterioration. The optimal triggering time of the DoS attack is deduced theoretically. Simulation results show that, while satisfying all physical constraints, the proposed strategy reduces the total economic benefit of the system from 3462.9 RMB to 2786.1 RMB, resulting in an economic loss of approximately 19.54 %. Furthermore, comparisons under different DoS attack timings verify the consistency between the optimal DoS attack timing and the scheduling sequence of the first two-stage data integrity attacks. This study confirms that an in-depth understanding of attack mechanisms is a key prerequisite for building targeted defense systems.