If your ceiling height is 8 feet tall then you want to space your recessed lights 4 feet apart in the kitchen to give optimal lighting from the recessed lighting.
If your ceiling is 10 feet tall in your kitchen then you want to space the recessed lighting 5 feet apart to help spread out the light.
My recessed lights in my kitchen with an 8 foot tall ceiling are spaced 4 feet apart and it gives great lighting.
The same goes with the rest of the house where you have recessed lighting space them 4 feet apart for 8 feet tall ceilings and 5 feet apart for 10 foot tall ceilings.