Most marine creatures exhibit remarkable flow sensing abilities. Their task of discerning hydrodynamic cues from local sensory information is particularly challenging because it relies on local and partial measurements to accurately characterize the ambient flow. This is in contrast to classical flow characterization methods, which invariably depend on the ability of an external observer to reconstruct the flow field globally and identify its topological structures. In this paper, we develop a mathematical framework in which a local sensory array is used to identify select flow features. Our approach consists of linearizing the flow field around the sensory array and providing a frame-independent parameterization of the velocity gradient tensor which reveals both the local flow ‘type’ and ‘intensity’. We show that a simple bioinspired sensory system that measures differences in flow velocities is capable of locally characterizing the flow type and intensity. We discuss the conditions under which such flow characterization is possible. Then, to demonstrate the effectiveness of this sensory system, we apply it in the canonical problem of a circular cylinder in uniform flow. We find excellent agreement between the sensed and actual flow properties. These findings will serve to direct future research on optimal sensory layouts and dynamic deployment of sensory arrays.