Distributed detection of informalion flows by timing analysis is considered. Timing measurements are subject, to perturbations and the insertion of chaff noise. Moreover, communications among distributed traffic sensors are subject to capacity constraints. With the assumption that the detector is colocated at a point of measurement, the problem is formulated as a distributed hypothesis testing with side-information. The main challenge is that there is no parametric model for the relaying of information flows. Under the assumption that the relaying of flows is subject to bounded delays, distributed detection systems are designed by converting a centralized detector to distributed detectors under slot-based quantization. The proposed systems are evaluated both theoretically and numerically by the proposed performance measure as a function of the capacity in data collection. Numerical evaluation shows that separately designing data compression and detection modules can achieve satisfactory overall performance.