We present flexible transmissive structural color filters with high-color-purity based on a higher-order resonance suppression by inserting an ultrathin absorbing layer in the middle of a cavity. A 3rd order Fabry-Pérot (F-P) resonance, which exhibits a narrower bandwidth than a fundamental F-P resonance, is used to produce transmissive colors with an improved color purity. The thin absorbing layer is properly placed at a center of the cavity to highly suppress only a 5th order F-P resonance appearing at a short wavelength range while not affecting the 3rd order F-P resonance for color generation, thus being able to attain the high-color-purity transmissive colors without reducing a transmission efficiency. In addition, angle-insensitive properties are achieved by compensating a net phase shift with a dielectric overlay and using a material with a high refractive index for the cavity medium. Moreover, the transmissive colors on a flexible substrate are demonstrated, presenting that changes in both the resonance wavelength and the transmission efficiency are nearly negligible when the color filters are bent with a bending radius of 5 mm and over 3000 times bending tests. The described approach could pave the way for various applications, such as colored displays, decorative solar panels, and image sensors.