Increasing the intermittent outputs of renewable energy sources (RESs) has forced planners to define a new concept named flexibility. In this regard, some short- and long-term solutions, such as transmission expansion planning (TEP) and energy storage systems (ESSs) have been suggested to improve the flexibility amount. A proper optimization procedure is required to choose an optimal solution to improve flexibility. Therefore, a mixed-integer linear programming (MILP) direct-optimization TEP versus ESSs co-planning model is presented in this paper to enhance power system flexibility. In doing so, a novel RES-BESS-based grid-scale system flexibility metric is proposed to investigate the improvement of flexibility amount via ESSs modules in the numerical structure. In this paper, a novel repetitive fast offline method has been proposed to quickly reach the desired amount of flexibility by defining an engineering price/benefit trade-off to finally find the best investment plan. Also, multiple uncertainties associated with wind farms and demanded loads and a practical module-type battery energy storage system (BESS) structure for each node are defined. The proposed model is applied to the modified IEEE 73-bus test system including wind farms, where the numerical results prove the model efficiency as BESS impacts on flexibility, investment plans and power system economics.