As multi energy-type demands are to be satisfied through physical energy flow networks, multi-energy flow (MEF) is fundamental for analyzing coupled energy flows in integrated energy systems (IES), which is of great significance to the optimal dispatch of integrated energy systems (IES). Therefore, we develop a day-ahead optimal scheduling approach for integrated energy systems (IES) in this paper, aiming at guaranteeing physical feasibility and economic viability of the coordinated scheduling results by considering multi-energy flow constraints. Specifically, based on the models of multiple energy coupling components, electricity network, natural gas network and hydraulic-thermal network, a decomposition-based sequential multi-energy flow calculation method for integrated energy system (IES) is developed to calculate energy flows within coupled electricity, heat, and gas sub-networks. Furthermore, we propose an optimal scheduling method which integrates the decomposed multi-energy flow calculation with the heuristic algorithm to derive day-ahead optimal scheduling results of coupled multi-energy systems. Numerous simulation results are given to illuminate the effectiveness and necessity of considering MEF constraints for the optimal scheduling of IES.