Kool-Aid does not have pork in it.
Gelatin however does have pork in it but Kool-Aid is gelatin free and pork free so that means that Kool-Aid is vegetarian.
From the standpoint that Kool-Aid is not made from any obvious products derived from animals, Kool-Aid is considered to be vegan.
However, this strictly refers to their flavored drink mixes because Kool-Aid also offers other product lines that are not vegan such as Kool-Aid Ice Cream Bars (contains dairy).
For a time, it was rumored that the popular drink mix contains gelatin, an animal protein, but the rumor is unfounded.
Formulations vary, but most flavors are some combination of simple sugars, citric acid, vitamin C, calcium phosphate, and artificial flavors and colors.
The ingredients of Kool-Aid Include Water, Citric Acid, Potassium Citrate, Gum Arabic, Sucralose (Sweetener), Contains Less than 2% of Artificial Flavor, Acesulfame Potassium (Sweetener), Sucrose Acetate Isobutyrate, Red 40, Blue 1, Sodium Benzoate and Potassium Sorbate (Preservatives).
So if you're vegetarian you can safely drink Kool-Aid as none of the ingredients in Kool-Aid are derived from animals.
The pork in Gelatin comes from the boiling of the bones.