Configuring energy storage systems (ESSs) in distribution networks is an effective way to alleviate issues induced by intermittent distributed generation such as transformer overloading and line congestion. However, flexibility has not been fully taken into account when placing ESSs. This paper proposes a novel ESS placement method for flexible interconnected distribution networks considering flexibility constraints. An ESS siting and sizing model is formulated aiming to minimize the life-cycle cost of ESSs along with the annual network loss cost, electricity purchasing cost from the upper-level power grid, photovoltaic (PV) curtailment cost, and ESS scheduling cost while fulfilling various security constraints. Flexible ramp-up/-down constraints of the system are added to improve the ability to adapt to random changes in both power supply and demand sides, while a fluctuation rate of net load constraints is also added for each bus to reduce the net load fluctuation. The nonconvex model is then converted into a second-order cone programming formulation, which can be solved in an efficient manner. The proposed method is evaluated on a modified 33-bus flexible distribution network. The simulation results show that better flexibility can be achieved with slightly increased ESS investment costs. However, a large ESS capacity is needed to reduce the net load fluctuation to low levels, especially when the PV capacity is large.