We demonstrate the multifolding Origami manufacture of elastically-deformable Distributed Bragg Reflector (DBR) membranes that reversibly color-tune across the full visible spectrum without compromising their peak reflectance. Multilayer films composed of alternating transparent rubbers are fixed over a 300 μm wide pinhole and deformed by pressure into a concave shape. Pressure-induced color tuning from the near-IR to the blue arises from both changes in thickness of the constituent layers and from tilting of the curved DBR surfaces. The layer thickness and color distribution upon deformation, the band-gap variation and the repeatability of cyclic color tuning, are mapped through micro-spectroscopy. Such spatially-dependent thinning of the film under elastic deformation produces spatial chirps in the color, and are shown to allow reconstruction of complex 3D strain distributions.