In service function chaining, data flows from a particular application or user travel along a pre-defined sequence of network functions. Appropriate service function chaining resource allocation is required to comply with the service level required by the application. In this paper, we introduce a dynamic priority assignment for flows that compete for service using a particular network function in a chain. Using the recent results of the performance metrics of transient birth-death processes, we analyse this priority assignment and develop an optimal strategy for selecting a (cheap) low-or (expensive) high-priority service, given the flow's service level agreement requirements. A decision table can, thus, be created to facilitate the fast, online priority scheduling of newly arriving flows requesting service.