Multi-radio multi-channel (MRMC) wireless mesh networks (WMNs) have emerged as the broadband networks to provide access to the Internet for ubiquitous computing with the support for a large number of data flows. Many applications in WMNs can be abstracted as a multi-flow coexistence problem to carry out multiple concurrent data transfers. More specifically, links in different channel layers must be concatenated to compose multiple data transfer paths based on nodes’ free interfaces and available channels. This is typically formulated as a combinatorial optimization problem with various stages including channel assignment, path computing, and link scheduling. This paper analyzes traffic behaviors and designs a coexisting algorithm to maximize the number of concurrent data flows. Simulations are conducted in combinatorial cases of channel and radio with various traffic requests of multiple pairs. The experimental results show the efficacy of the coexisting algorithm over a randomly generated topology. This scheme can be used to develop routing and scheduling solutions for various multi-flow network applications through prior computing.