Yes you can bring your own snacks on the plane with you to eat while on the plane.
I've taken bags of chips, candy and other snacks on the plane without a problem.
You can also take pies, cakes etc or any other food items on the plane and they'll be allowed through the checkpoint through TSA.
So bring any snacks you want to on the plane with you and they will be allowed through the airport checkpoint.
They just need to go through the screening and you can bring the snacks onto the plane in your checked or carry on luggage.
All food items are allowed on airplanes in checked luggage or carry on luggage as long as none of the food items are liquids in amounts exceeding 3.4 ounces.