Answer: Yes, there is. Any note can be flatted, even C and F. The note "C flat" on the piano is played on the same key used for B.

Similarly, there is such a thing as B sharp and E sharp. B sharp is played on the same key used for C.

A flat always lowers a pitch one half-step, regardless of where you start. At one time there were experimental keyboards made that used separate keys for these different note names, and tuned them slightly differently! But on the modern keyboard they are are the same pitch.