In the global low-carbon energy transition, the integrated energy system （IES）, as the key to achieving the "dual carbon" goal, faces two core challenges: the limitations of traditional carbon accounting methods and dynamic carbon management of multi energy flow coupled systems. Traditional carbon accounting methods are difficult to capture the impact of fluctuations in new energy output and time-varying load characteristics on carbon flow due to static carbon emission factors, resulting in unfair allocation of carbon emission responsibilities. The dynamic carbon management of multi-energy flow coupled systems faces difficulties in tracking cross energy carbon emissions and high complexity of dynamic models. In response to the above challenges, a dynamic carbon flow propagation theoretical framework is proposed, which includes two aspects: 1） A multi-energy flow coupled matrix and time-varying node carbon intensity （TV-NCI） is constructed, and a dynamic carbon index is constructed, and the impact of new energy output fluctuations and time-varying load characteristics on carbon flow changes is analyzed, a new solution is provided for cross energy carbon emission tracking in multi-energy flow coupled systems. 2） By introducing the carbon flow betweenness centrality （CFBC） index, the impact of grid structure on carbon flow paths is analyzed and the key nodes that affect carbon transmission is identified. Through experimental verification of the IEEE 33-node extended system, the proposed method effectively reduces carbon emissions and new energy curtailment rates, and reveals the impact of network topology on carbon propagation paths. The research results provide theoretical support for the low-carbon planning and operation of IES.