We consider the problem of clandestine communications, i.e., communications that are meant to be invisible to third-party eavesdroppers, in the context of wireless sensor networks. Although encryption and anonymous routing protocols can hide the content and the routing information, the transmission activities of sensors on the same route can still reveal the information flow. In this work, a perfectly clandestine scheduling method is developed to hide the desired information flow in a sequence of independent transmission activities resembling those without any flow, while satisfying the resource constraint at the relay nodes in terms of limited buffer size. The proposed method is proved to achieve the maximum throughput, which is characterized analytically for transmission schedules following alternating renewal processes with a closed-form solution for Poisson processes. The analytical results are verified through numerical simulations on synthetic traffic as well as traces.