We introduce a systematic approach for designing ultrathin, flexible, and polarization-insensitive metasurface absorbers (MSAs), suitable for aviation applications, such as radar cross-section reduction of unmanned aerial vehicles. Metal-backed resistive patches are arranged on a flexible polyethylene terephthalate substrate of thickness about 1/100 of the operating wavelength, classifying the absorbers as ultrathin. The ultralow weight of the proposed MSAs is crucial for the targeted aviation applications, to ensure airworthiness. A narrowband uniform MSA is designed to achieve maximum absorption and serves as a starting point to synthesize a broadband and polarization-insensitive $3 \times 3$ absorber supercell. The non-uniform absorber is systematically designed by a fast semi-analytical method. The proposed absorbers have been fabricated and experimentally tested both on flat and cylindrical curved surfaces, with measurements being in very good agreement with the corresponding simulations, and corroborate the high absorption and broadband behavior of the proposed non-uniform ultrathin and flexible absorber.