The ability of a swimming robot to extract information from a vortex field in the ambient fluid flow has immense practical applications. Such capabilities perhaps augmented with other sensors are useful to detect and avoid obstacles or potential adversaries in the fluid. This has led many researchers to attempt to sample the pressure field on the surface of a swimmer and thus extract information about the fluid flow such as the flow velocity and angle of attack. In contrast in this paper, we show through simulations, that the kinematic information of a swimmer, specifically its angular velocity, can be used to train a neural network, that can classify the vortex wake in the surrounding fluid. In effect, this classifies the type of body (or its motion) that generates the ambient wake. In practice, the angular velocity of a body can be measured with much greater accuracy than the pressure distribution on the body. We further show that a swimmer with a passive tail-like appendage can classify the vortex field with greater accuracy than a swimmer without such an appendage. Thus the results demonstrated in this paper can be of significant use in designing aquatic robots with passive appendages with improved capabilities of sensing and classifying the ambient flow.