The tablet has all the allergy info. They do have gf options, but they say that they make everything in a shared kitchen. I felt ok eating it as there really weren’t many other options in the terminal.
At the time I am writing this there are 3 Farmer's Fridges in terminal 4 at jfk. Very few gf options in this terminal. The touch screen menu for the containers in the fridge show you dietary / allergy information. I had the Burrito Bowl which is marked as not containing gluten or dairy I added the separate chicken bowl to it. Pretty tasty and didn't get sick. NOTE you will have to provide your own utensils or get some at a restaurant.