Under the strain of global warming and the constant depletion of fossil energy supplies, the power system must pursue a mode of operation and development with minimal carbon emissions. There are methods to reduce carbon emissions on both the production and consumption sides, such as using renewable energy alternatives and aggregating distributed resources. However, the issue of how to reduce carbon emissions during the transmission of electricity is ignored. Consequently, the multi-objective optimal carbon emission flow (OCEF) is proposed, which takes into account not only the economic indices in the conventional optimal power flow (OPF) but also the reduction of unnecessary carbon emissions in the electricity transmission process, i.e., carbon emission flow losses (CEFL). This paper presents a deep reinforcement learning (DRL) based multi-objective OCEF solving method that handles the generator dispatching scheme by utilizing the current power system state parameters as known quantities. The case study on the IEEE-30 system demonstrates that the DRL-based OCEF solver is more effective, efficient, and stable than traditional methods.