Thermal metamaterials are artificial materials used to manipulate heat flow in many applications, such as thermal protection, thermal camouflage, and precise temperature control. Most of the existing thermal metamaterials are mainly based on metal, which makes their fabrication complex and time-consuming, and limits their flexibility. Here, we show a strategy to simplify the fabrication process, improve machining accuracy, and realize flexibility in thermal metasurfaces. Our proposed thermal metasurface is fabricated by laser engraving of copper-graphene coating surface, utilizing graphene coating with high thermal conductivity instead of the traditional filling materials of low thermal conductivity. It maintains the integrity of copper substrate, giving the metasurface a good heat dispersion. Controlled temperature gradient patterns are established, and the metasurface can be bent without changing its features, except for a slight variation in its thermal gradient. Finally, its cloaking ability is demonstrated by camouflaging the same heat source in the shape of different objects. Our designed metasurface mitigates the limitations in design and fabrication of existing thermal metamaterials, and can be used in applications requiring large flexibility, thermal illusion, and large thermal gradients on small scales.