Kenny asks for more Kool-Aid because he has a peanut butter and jelly sandwich that has too much peanut butter on it. Regardless of how the Kool-Aid tastes, it is better to have something to drink when eating such a sandwich.
In Chapter 10, the Watson family is driving down to Birmingham and has just entered Ohio. They are stopped at a rest area for lunch. Momma has made Kool-Aid using water from a pump at the rest area. The Kool-Aid taste metallic and like medicine. Everyone except Momma hates it and they all dump theirs out when she isn’t looking. But Kenny is having a peanut butter and jelly sandwich. This means that he needs the Kool-Aid because
Momma always puts too much peanut butter on the sandwich and you’ve got to have something to wash it down in case you start choking.
So, even though Kenny hates the Kool-Aid, he asks for seconds because he dumped his first cup but needs something to drink with the sandwich.