The increasing penetration of converter-interfaced renewable energy sources has led to a reduction in system inertia and has intensified frequency stability challenges in modern power systems. Battery energy storage systems (BESSs) can provide fast active power support. However, their effectiveness depends on installation location, power rating and network operating conditions. This paper proposes a power flow informed sensitivity based method for the placement and sizing of distributed BESSs to improve frequency nadir performance in low-inertia power systems. The proposed method combines marginal frequency sensitivity obtained from time domain screening simulations with network coupling information derived from power flow. These components are integrated into an optimization formulation subject to practical installation constraints and solved using particle swarm optimization. The method is evaluated using time domain simulations on the IEEE 39-bus New England test system under multiple generator outage contingencies. The results show that BESS locations exhibit non-uniform and nonlinear contributions to frequency nadir and rate of change of frequency improvement. The proposed optimal placement and sizing method distributes BESS capacity across multiple buses based on frequency impact and network coupling. Compared with the baseline case and a benchmark metaheuristic optimal placement and sizing method, the proposed method achieves higher frequency nadirs and lower RoCoF values across all evaluated contingencies. The performance is maintained under load variation scenarios and reduced system inertia due to renewable energy integration. The proposed method provides a physically meaningful and computationally efficient approach for allocating distributed BESSs to support frequency stability in low-inertia power systems.