In this paper, we introduce Vision Tape (VT), a novel class of flexible compound-eye-like linear vision sensor dedicated to motion extraction and proximity estimation. This novel sensor possesses intrinsic mechanical flexibility that provides wide-range adaptive shape, allowing adjustable field of view as well as integration with numerous substrates and curvatures. VT extracts Optic Flow (OF) of the visual scene to calculate the motion vector, which allows proximity estimation based on the motion parallax principle. In order to validate the functionality of VT, we have designed and fabricated an exemplary prototype consisting of an array of eight photodiodes attached to a flexible PCB that acts as mechanical and electrical support. This prototype performs image acquisition and processing with an integrated microcontroller at a frequency of 1000 fps, even during bending of the sensor. With this, the effect of VT shape on motion perception and proximity estimation is studied and, in particular, the effect of pixel-to-pixel angle is discussed. The results of these experiments allow estimating an optimal configuration of the sensor for OF extraction. Subsequently, a method that enhances the quality of extracted OF for non-optimal configurations is proposed. The experimental results show that, by applying the proposed method to VT in a suboptimal curvature, the quality of the OF can be increased by up to 176% and proximity estimation by 178%.