We demonstrate a flexible transmissive color filter based on a hybrid metallic-optical Tamm state device composed of a thin metallic film on top of dual dielectric distributed Bragg reflectors (DBRs) to simultaneously excite the Tamm plasmon (TP), the optical Tamm state (OTS), and the Fabry-Pérot (FP) resonant eigenmodes for spectrally achieving triple transmittance peaks in the visible light range. We show that the resonant eigenmodes confined inside the device can be tuned at will by simply adjusting the designed Bragg wavelengths of the dual DBRs and retain an ultranarrow bandwidth regardless of resonant wavelength, creating the desired chromaticity points and constructing a large color gamut space in the CIE coordinate. We further show that, due to the fabrication simplicity of our color filter involving only thin-film deposition, the proposed structure can be easily integrated onto flexible substrates, leading to tunable transmittance spectrum as well as the color appearance by simply changing its bending curvature. The tunable color filter reported herein can be employed for various applications such as aesthetical color decorations in architectures, low-cost and portable spectral analyzers, and optical strain/deformation sensors.