I did Bike Across Kansas last year and we never did find the flats. What we found is that on the west edge, the hills last for 4 miles. If you look at the terrain map of Kansas on google maps, you'll see that most of it isn't really flat.

And when you do get out to where it is flatter, you have the winds to battle. No matter what direction you are going, it seems like you have a stiff breeze.