Magnetic skyrmions are topological spin swirls possessing intriguing electromagnetic properties. The integration of skyrmion materials into flexible substrates has led to the development of flexible spintronics with high performance. However, research into flexible skyrmion materials remains limited. Here, we report the growth of [Pt/Co/Ta]10 multilayer, a typical system hosting skyrmions, on multiple flexible substrates. By combining atomic force microscopy with magnetization measurements, we establish a correlation between surface morphology and perpendicular magnetic anisotropy. The field-driven evolution of skyrmions is also discussed. Additionally, to explain the observed differences in magnetic domain structures of samples grown on flexible substrates and Si substrates, the relationship between magnetic domain width and the variations in magnetic parameters is investigated. Our findings reveal that skyrmion materials can be grown on diverse flexible substrates and tuned by substrate morphology, which shows promising prospects for wearable flexible spintronic devices.