When you go to Six Flags they don't let you go in with food, especially a cooler. They check your purses and diaper bags (of course with changes of clothes and diapers, etc). If you have a baby they'll allow in baby food because they don't provide that sort of thing, or if you have a child with food allergies, but you can't bring more than a snack-sized amount of anything. They also prefer that you purchase drinks in the park.
HOWEVER you can pack a cooler full of food and drinks and leave it in your car. You can go back and forth to your car as many times as you want for a snack, lunch, or whatever.
If you carry in stuff for the water park, but want to walk around for a while, you can rent out lockers to hold all of your stuff.