Flexibility isn't the issue though it's repeat flexing. Copper wire will work harden with repeat flexing and break regardless of how fine it is, so the material is critical, whatever the alloy it is it has to be designed to avoid work hardening. The only tip I can give is that what you want is elasticity not plasticity. Common copper conductive wire is a very plastic material but work hardens because of it's nearly pure crystalline structure, you need something that will give again and again because of it's structure, it's going to be an alloy of some kind.