To address the inaccurate characterization of thermal storage carbon emission flow in integrated energy systems (IES) and to enhance the flexibility of both supply and demand sides across multiple energy parks, this paper proposes a low-carbon economic dispatch method for multi-park IES, which considers the augmented carbon emission flow of thermal storage. First, based on the heat dissipation effect of thermal storage, an augmented carbon emission flow of thermal storage is established. Second, on the supply side, the organic Rankine cycle (ORC) is used to achieve flexible thermal and electrical output from combined heat and power (CHP) units, while on the demand side, the transferability and substitutability of electricity, heat, and gas loads are considered, to construct a dual-response low-carbon model of multi-park IES. Finally, a bi-level low-carbon economic dispatch strategy is formulated, aiming to minimize the upper-level electricity-gas network scheduling cost and the lower-level energy hub cost, which includes energy procurement, carbon trading, and demand-side response. Through scenario-based simulation analysis, the results demonstrate that the low-carbon economic dispatch strategy reduces the total operational cost of the multi-park IES by 3.51% and carbon emissions by 8.72%.