Emerging applications across environmental, biomedical, and structural monitoring require the measurement of physical variables over extended regions. Because addressing many sensors individually can result in impractical bandwidth and power requirements, there is a need for distributed sensing approaches wherein readouts are obtained directly at the ensemble level. In turn, this generally requires sensor nodes capable of interacting with each other to implement the required readout statistic. Here, the first practical steps towards approaching this challenge via a nonlinear analog approach based on chaotic synchronization are presented. Namely, single-transistor oscillators, representing remarkably low-complexity yet highly-flexible entities, are experimentally found to be suitable for wireless coupling via mutual induction, realizing a simple form of telemetry for luminous flux. Via numerical simulations and numerous laboratory experiments, a rich repertoire of possible interactions among multiple sensor nodes and between the same and an external exciter is demonstrated, encompassing synchronization, desynchronization, relay effects, and chaotic transitions. Together, these results reveal the possibility and means of accurately estimating the average of a distributed physical magnitude from the complexity of ensemble dynamics. This new approach contributes an important blueprint for future work using simple chaotic circuits in sensing applications.