Estimating the direction of ambient fluid flow is key for many flying or swimming animals and robots, but can only be accomplished through indirect measurements and active control. Recent work with tethered flying insects indicates that their sensory representation of orientation, apparent flow, direction of movement, and control is represented by a 2-dimensional angular encoding in the central brain. This representation simplifies sensory integration by projecting the direction (but not scale) of measurements with different units onto a universal polar coordinate frame. To align these angular measurements with one another and the motor system does, however, require a calibration of angular gain and offset for each sensor. This calibration could change with time due to changes in the environment or physical structure. The circumstances under which small robots and animals with angular sensors and changing calibrations could self-calibrate and estimate the direction of ambient fluid flow while moving remains an open question. Here, a methodical nonlinear observability analysis is presented to address this. The analysis shows that it is mathematically feasible to continuously estimate flow direction and perform regular self-calibrations by adopting frequent changes in course (or active prevention thereof) and orientation, and requires fusion and temporal differentiation of three sensory measurements: apparent flow, orientation (or its derivative), and direction of motion (or its derivative). These conclusions are consistent with the zigzagging trajectories exhibited by many plume tracking organisms, suggesting that perhaps flow estimation is a secondary driver of their trajectory structure.