The problem of detecting multi-hop information flows subject to communication constraints is considered. In a distributed detection scheme, eavesdroppers are deployed near nodes in a network, each able to measure the transmission timestamps of a single node. The eavesdroppers must then compress the information and transmit it to a fusion center, which then decides whether a sequence of monitored nodes are transmitting an information flow. A performance measure is defined based on the maximum fraction of chaff packets under which flows are still detectable. The performance of a detector becomes a function of the communication constraints and the number of nodes in the sequence. Achievability results are obtained by designing a practical distributed detection scheme, including a new flow finding algorithm that has vanishing error probabilities for a limited fraction of chaff packets. Converse results are obtained by characterizing the fraction of chaff packets sufficient for an informati...