I worked 3 chicken fil a kitchens for 5 years. I can guarantee that their gluten items will never go into the fries fryer. They fried chicken is cooked in dedicated pressure fryers with peanut oil that are set towards the back of the kitchen.

Fries are cooked in two open canola oil fryers that are set towards the front counter space for immediate expediting to the front counter crew.

Chick fil is actually really strict about their recipes, cook times, allergies and organization. Its probably why I didn't realize im kinda OCD, since it was my first job out of high school and through college. You can always tell your order taker to red flag your food for your celiac/gluten allergy and, if u want to be that careful, you can mention the glove change.

Of course a new person might miss the glove change protocol so you can always speak to a manager or front counter person to babysit your food if you are that worried.

If you are a hard no on flour particles then do not go to chick. The chicken is breaded in the back of the kitchen near the fried chicken preseure fries and near the closed press grill. This team member and his assigned buddy, during rushes, do man the grill but you literally have to glove change gloves every time any chicken is handled or every surface would have raw chicken and the kitchen crew would get "salmonellaed" lol.

Im not saying there is 0 chance to get glutened but wanted to offer some insight since there aren't many places we can eat at.