Accurate multi-angle spectropolarimetry permits the detailed and unambiguous characterization of a wide range of objects. Science cases and commercial applications include atmospheric aerosol studies, biomedical sensing, and food quality control. We introduce the FlySPEX spectropolarimetric fiber-head that constitutes the essential building block of a novel multi-angle sensing system. A combination of miniaturized standard polarization optics inside every fiber-head encodes the full linear polarization information as a spectral modulation of the light that enters two regular optical fibers. By orienting many FlySPEX fiber-heads in any desired set of directions, a fiber bundle contains the complete instantaneous information on polarization as a function of wavelength and as a function of the set of viewing directions. This information is to be recorded by one or several multi-fiber spectrometers. Not only is this system flexible in the amount of viewing directions and their configuration, it also permits multiplexing different wavelength ranges and spectral resolutions by implementing different spectrometers. We present the design and prototyping for a FlySPEX fiber-head that is optimized for both polarimetric accuracy and commercial series production. We integrate the polarimetric calibration of each FlySPEX fiber-head in the manufacturing process.