The increasing penetration of renewable energy sources (RES) in power systems poses significant challenges for low-carbon economic dispatch due to their inherent variability and the complexity of carbon emission propagation paths. Existing methods struggle to accurately quantify RES uncertainty costs, and traditional carbon pricing mechanisms fail to effectively trace the indirect carbon emissions induced by RES fluctuations. To address these issues, this study proposes a multi-objective optimization framework integrating uncertainty cost modeling based on information theory and dynamic carbon flow allocation. Firstly, an information entropy-based RES uncertainty cost model is designed. This model resolves the challenge of RES participation in unit commitment due to their near-zero marginal costs by equitably allocating uncertainty risks via Shapley value. Secondly, a carbon flow-driven dynamic bus carbon intensity allocation model is developed to precisely trace the propagation paths of additional carbon emissions caused by RES power deviations. Thirdly, an Multi Modal NSGA-III (MMNSGA-III) algorithm is proposed to coordinate the trade-offs between the uncertainty cost model and the dynamic carbon allocation mechanism. This algorithm employs dynamic reference points and multi-modal strategies to effectively navigate RES-induced fragmented decision spaces, ensuring pareto solutions that simultaneously minimize uncertainty costs and emission propagation.