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A pure inorganic flexible magnetic thin film that is transparent with high temperature and light weight is crucial for high temperature flexible/wearable magnetic sensors and spintronics devices such as electronic skin and a mechanical arm. Here, a transparent flexible Hf0.95Co0.05O2 (HCO) thin film with various thicknesses of 105, 140, 175, and 210 nm was deposited on fluorophlogopite (F-Mica) substrates by using a sol-gel method. All of the flexible HCO samples show two phase structures with a monoclinic phase (M-phase) and an orthorhombic phase (O-phase), resulting in strain and strain relaxation in the samples of different thicknesses. An out-of-plane anisotropy behavior in saturation magnetization was observed in the flexible HCO samples, and the values of (Ms-out-of-plane−Ms-in-plane) decrease with the increase in the thickness. The content of Co2+ increases and the content of Co3+ and vacancy oxygen decrease when the thickness increases, which will affect the anisotropic magnetization behavior in the flexible HCO thin films. Moreover, the flexible HCO samples show excellent light transparency (above 80% in the visible range). The flexible HCO thin films with an anisotropic magnetization behavior and high transmittance are promising for various applications in transparent flexible/wearable devices.