Abstract—This paper presents a three-phase optimal power flow (TOFP) based method for mitigating the voltage unbalance factor (VUF) in each of the three-phase busbars with the help of demand-side flexibility. It can be expected that issues with the unbalanced voltage can increase in the future distribution system with significant levels of single-phase Distributed Energy Resources (DERs). Unhealthy voltage unbalance status reduces the efficiency of the distribution systems, leading to energy loss and heat problems in electrical devices. This paper has proposed a three-phase OPF (TOPF) based local flexibility market (LFM) framework, where Distribution System Operators (DSOs) can utilize the upwards or downwards flexibility to manage the voltage unbalance. A modified IEEE-34 bus distribution network is used to illustrate the implementation of the proposed methodology, with the simulation results showing that the VUF value varies with the unbalanced load and connected photovoltaic (PV) levels, while the VUF drops below the limiting threshold when the flexible phase-by-phase flexibility services are introduced. This means that the proposed approach could inform modification of flexible service product in the future local flexibility market framework to help DSOs mitigate the unbalanced voltage.