This study investigates the crystal structure, epitaxial relation, and magnetic properties in CoFe thin films deposited on a flexible mica substrate. The epitaxial growth of CoFe thin films was successfully achieved by DC magnetron sputtering, forming three CoFe(002) domains exhibiting four-fold symmetry on the mica substrate. A notable achievement of this work was the attainment of the highest anisotropic magnetoresistance (AMR) value reported to date on a flexible substrate. Additionally, it was observed that the magnetic characteristics of the CoFe films on the flexible mica substrate display reversibility upon strain release. More importantly, the AMR effect of epitaxial CoFe films on flexible mica shows lesser dependence on the crystalline orientation and remains the same under different bending states. These findings demonstrate the potential of utilizing CoFe films on flexible substrates to develop wearable magnetoresistance sensors with diverse applications.