In monitoring flows at routers for flow analysis or deep packet inspection, the monitor calculates hash values from the flow ID of each packet arriving at the input port of the router. Therefore, the monitors must update the flow table at the transmission line rate, so high-speed and high-cost memory, such as SRAM, is used for the flow table. This requires the monitors to limit the monitoring target to just some of the flows. However, if the monitors randomly select the monitoring targets, multiple routers on the route will sometimes monitor the same flow, or no monitors will monitor a flow. To maximize the number of monitored flows in the entire network, the monitors must select the monitoring targets while maintaining a balanced load among them. We propose an autonomous load-balancing method where monitors exchange information on monitor load only with adjacent monitors. Numerical evaluations using the actual traffic matrix of Internet2 show that the proposed method improves the total monitored flow count by about 50% compared with that of independent sampling. Moreover, we evaluate the load-balancing effect on 36 backbone networks of commercial ISPs.