Usually flexibility is a function of how thin you can make something and what physical shape it has. You can shape it such that it becomes less flexible (think I beam for an example) or you can shape it so that it becomes more flexible (think foil). It's all the same material but the mechanical properties can be quite different. Practical use superconductor material is typically in a ribbon form, this allows for relatively easy shaping along one axis and still allows you to connect to it in a (relatively) simple way. An extra advantage of using a ribbon like conductor is that it allows for very close spacing without much loss in packing. Think 'oranges' versus 'boxes'.