I have done a lot of flying out of Kansas City and my top priorities when flying to Disney are the lowest price and the flight with the best times. We always choose to fly out of Kansas City as early as possible so that we can get into Orlando early and get to enjoy the day at Disney. Then on the way home to Kansas City, I always choose the latest flight possible. I want to stay as long as possible!
Tip: Book as early as possible! You may be able to find some direct flights with no layovers. Who wants to waste time sitting in an airport when you can be waiting in line for Splash Mountain? Even if you don't get a flight you want, keep an eye on flights to see if any seats open. I don't think the saying "Money is Time" applies better to any situation!
So which airline is my absolute favorite? Southwest! I have a cute story about great customer service from Southwest when my husband and I were traveling to Orlando for our Disneymoon. When the Southwest team discovered that we were honeymooners, they created a veil and crown out of their peanuts and those plastic swords that they serve olives on in drinks. They also had toilet paper hanging off of them. They announced us as newlyweds on the PA and put the hats on our heads and then gave us a bottle of champagne that was addressed to us! We still have it and plan to drink it on a special anniversary. It really made us feel really special.
But this story is just one reason I love Southwest, there are many other reasons. First of all they offer a lot of flights out of Kansas City. Many of them are nonstop as well. They have an extra early flight that we usually take to Disney that I also like. They also seem to be the cheapest whenever I am looking! If their price goes down you can call them and the amount that it was reduced will be refunded to you. You can't beat that! Also, bags are free! I just don't think you can beat Southwest.
And maybe if you are lucky, maybe you will run into this guy!