Could you please clarify your question? As per my understanding, you are saying that the driver by ST does not extend support for S25FL256S and it needs to be fixed. I would like to suggest you to contact ST Microelectronics for that.
I would also like to inform you that Cypress has its own low level driver for its serial flash devices. I am attaching the driver with my response. You can go through it and use it in you project if you want.