I was so thrilled to hear that Dairy Keen does celiac safe food. The owners themselves have celiac and the employees are very understanding and considerate. I have eaten here over a dozen times and never gotten sick. They have a gluten free fryer and food comes in a separate bag/tray with a red 'allergy' sticker on it.
Here is a link to their gluten free menu. https://www.dairykeen.com/pdf/Dairy-Keen-Gluten-Free-Menu.pdf
If you aren't sure about something ask!
— Very
— Separate gluten-free menu
— Some
— Excellent