The following weekend is open, but the Chiefs don't have their schedule yet either. I'd probably plan on being flexible if I intended to cook the Royal.
I would imagine it will be the week before. The week after is also the baseball postseason, and given the bizzaro world we live in where my Royals are freaking World Champions, it would stand to reason that they want to keep that weekend open for home games.
The following weekend is open, but the Chiefs don't have their schedule yet either. I'd probably plan on being flexible if I intended to cook the Royal.
The KC Chiefs schedule will not be released by NFL until 3rd week of April, so I don't think there will be any decisions made before then. It's my understanding that the KC Royals have first dibs to the "whole" complex, so everything will center around them, before the Chiefs/American Royal have a say in it.