Concealed carry laws can be very strange sometimes, in that even if you have a permit to carry a concealed handgun, most of the time this has no effect on the legality of carrying other weapons. Kansas is one of those states.
The relevant statute for you is part of the Kansas Criminal Code, Section 21-4201 (I am not going to paste all that text in there, but I have provided an official link below you can use).
Subsection (a)(1) makes it illegal to possess or carry a "bludgeon" which is a very vague term. Like so many laws, the code does not define what this term means. Personally I would feel a baton is not a bludgeon because they are not intended to strike a person's head (which is deadly force). But it's not my opinion that matters, it is your local prosecutor's. Here is something to consider though: Look at local security guards in your area. Do they carry batons on their belts? If so, then batons are likely not covered under "bludgeon" because there is no exception under law for security guards to that part of the statute, and they would have been arrested by now.
Subsection (a)(2) makes it illegal to carry concealed OR carried with intent to hurt some one illegally, a "billy, blackjack, slungshot." The latter two items are weighted leather clubs, but the term "billy" in legal jargon usually refers to all manner of police baton (both fixed wooden ones and modern collapsible kinds). So, technically it would not be legal for you to carry a baton concealed under this statute. Yes, you could carry openly technically speaking, but why would you do that? It shows the baddies what you're packing, plus cops will give you crap about it anyway.
Wish I had better news than that. I applaud your intent to carry a less-lethal implement to compliment your handgun, because deadly force is not always the right course of action. Maybe consider high-grade pepper spray? It does work (I have used it) and it's perfectly legal.
