We demonstrate chirped Bragg gratings fabrication in doped microstructured tapered polymer fibers by using a uniform phase mask. The use of high photosensitive benzyl dimethyl ketal (BDK) doped core fiber allows to obtain chirped Bragg gratings by means of a single krypton fluoride laser pulse. The stability of the gratings has been confirmed and the strain and temperature sensitivity measurements demonstrate their tunable properties. Finally, different tapered profiles have been implemented in order to show the potentiality of this fabrication technique in polymer optical fibers.