I will add my two cents here.
There are a lot of great gravel tires on the market now thanks to the popularity of Dirty Kanza, but I have only worked with two models in the Flint Hills: Maxxis Ramblers and Donnelly MSO, both 700x40.
Both have been great, but ultimately I have chosen to stick with the Ramblers as they are tubeless and the first rule of DK tires is to go tubeless. In addition I would not go smaller than a 40 simply because of the added stability and comfort - it is a LONG day in the saddle and it adds up when you are riding a more narrow tire. The other two tires I know I have heard good feedback on are the Panaracer Gravel Kings and the Schwalbe G Ones - both are beloved by those who ride in the Flint Hills. But I can not speak from direct experience, just from friends who live in Emporia and have put miles on both of those tires. The best advice I can give is to go tubeless and just do some research, there are so many models to chose from if you find one that is described as good for the Flint Hills, or the Dirty Kanza, or has reviews about durability, you will probably be good to go.
Ride bikes and stay young.