Distributed detection of information flows spanning many nodes in a wireless sensor network is considered. In such a system, eavesdroppers are deployed near several nodes in the network. As data may be encrypted or padded, the eavesdroppers can only measure packet timestamps. Each eavesdropper, given a sequence of timestamps, must compress the information for transmission to a fusion center. Given the compressed data, the fusion center must decide whether the monitored nodes are part of an information flow. Information flows may be embedded with chaff noise, and packets may be perturbed by a random but bounded delay. A specific quantizer and algorithmic detection scheme are proposed. Performance is characterized by the maximum fraction of chaff that may be inserted in an information flow while still achieving vanishing error probabilities. A lower bound on the performance of the optimal system is derived. An upper bound on the performance of a system using the proposed quantizer is also found.