The limited predictability and controlability of distributed energy resources has resulted in an increasing need for managing the available demand side flexibility from proactive end-users. In this regard, distribution system operators are expected to take a coordinating role in facilitating the utilization of the available flexibility. This paper proposes a novel optimization method to solve the optimal flexibility dispatch problem for a system operator such that it deploys the demand response resource effectively. We use the second-order cone relaxation of the problem to keep the problem convex, tractable and representing electric flows to a high accuracy. The analytical solution to the problem gives the locational pricing of flexibility services. To demonstrate the applicability and scalability of the proposed framework, it is applied to two case studies. We study a stylized 9-bus distribution network and a modified version of the IEEE 30-Bus System. Simulation results are interpreted in economic terms and show the effectiveness of the proposed approach.