Although numerous studies have investigated low carbon optimization for park integrated energy system (PIES) under dual-carbon goals, few have proposed strategies to enhance carbon efficiency from carbon flow analysis. Therefore, a cloud platform-based low carbon economic operation strategy for PIES is proposed, considering carbon flow optimization. Firstly, a two-layer collaborative optimization architecture is constructed, where the upper-layer cloud platform designs a carbon flow optimization module to provide suggestions to the lower-layer PIES, then the lower-layer cloud platform adjust their energy consumption plans for collaborative optimization. Secondly, the load carbon potential indicator is developed to measure the carbon flow of PIES, guiding them through the cloud platform to reduce load carbon potential and improve system carbon emission efficiency. Additionally, a Nash bargaining module incorporating carbon efficiency is designed to maximize participants' benefits of multi-subject transactions. Then the target cascade analysis method is applied to solve the two-layer model. Finally, simulation results verify that the PIES operation strategy considering carbon flow optimization can reduce carbon emissions, improve carbon efficiency, and enhance economic benefits while promoting energy trading between PIES and increasing carbon profits.