Overlay networks which are dynamically created over underlying IP networks are becoming widely used for delivering multimedia contents since they can provide several additional user-definable services. Multiple overlay paths between a source-destination overlay node pair are designed to improve service robustness against failures and bandwidth fluctuation of the underlying networks. Multimedia traffic can be distributed over those multiple paths in order to maximize paths' utilization and to increase application throughputs. Most of flow-based routing algorithms consider only common metrics such as paths' bandwidth or delay, which may be effective for data applications but not for real-time applications such as Voice over IP (VoIP), in which different levels of such performance metrics may give the same level of the performance experienced by end users. This paper focuses on such VoIP overlay networks and proposes a novel alternative path based flow routing algorithm using an application-specific traffic metric, i.e. "VoIP Path Capacity (VPCap)," to calculate the maximum number of QoS satisfied VoIP flows which may be distributed over each available overlay path at a moment. The simulation results proved that more QoS-satisfied VoIP sessions can be established over the same multiple overlay paths, comparing to traditional approaches.