Burgers are pretty good, they have gluten free buns without an upcharge and will change gloves, etc. Fries are technically gluten free but in a shared fryer - the staff pointed this out to me without my even asking which is a good sign that they work hard to avoid cross contamination.
However - I'm uncertain if all of their sauces, especially for some of their more unusual burgers, are gluten free. The staff wasn't sure either so you may want to stick to more traditional toppings.
— Somewhat
— No gluten-free information on the menu
— Some
— Good