I use Trio mashed potatoes without milk, the kids at camp are asking if these are gluten free?

Trio used to be produced by Carnation, then Nestle and now I think they are part of the JR Simplot group. Simplot's Traditions mashed potato ingredients list contains no gluten products.

Ingredients:IDAHO® POTATOES, VEGETABLE OIL (SOYBEAN, CANOLA, COTTONSEED AND/OR SUNFLOWER), SALT, CONTAINS 2% OR LESS OF: NONFAT DRY MILK, BUTTERMILK POWDER, SPICE, DEXTRIN (SOLUBLE DIETARY FIBER), MODIFIED POTATO STARCH (SOLUBLE DIETARY FIBER), POTATO MALTODEXTRIN, EMULSIFIERS (MONO AND DIGLYCERIDES, CALCIUM STEROYL LACTYLATE), FLAVORS (NATURAL AND ARTIFICIAL FLAVOR, LACTIC ACID), TO PROTECT COLOR & FLAVOR (SODIUM ACID PYROPHOSPHATE, SODIUM BISULFITE, CITRIC ACID, TOCOPHEROLS), ARTIFICIAL COLOR. CONTAINS: MILK, SULFITES.

Idahoan has a section on their web site for gluten free mashed potatoes.

Basic American has several mashed potato products that are gluten free also.

Look over the required list of ingredients and search for potato flour or potato starch instead of wheat or just "flour".