This paper investigates a service deployment model for network function virtualization which handles per-flow priority to minimize the deployment cost. Service providers need to implement network services each of which consists of one or more virtual network functions (VNFs) with satisfying requirements of service delays. In our previous work, we studied the service deployment model with per-host priority; flows belonging to the same service, for the same VNF, and handled on the same host have the same priority. We formulated the model as an optimization problem, and developed a heuristic algorithm named FlexSize to solve it in practical time. In this paper, we address per-flow priority, in which flows of the same service, VNF, and host have different priorities. In addition, we expand FlexSize to handle per-flow priority. We evaluate per-flow and per-host priorities, and the numerical results show that per-flow priority reduces deployment cost compared with per-host priority.