My partner has never gotten sick here. They use a clean knife, clean gloves, and put the bread on a clean serving tray to make the sandwich. That being said, they do not use fresh knives for the condiments that are in buckets, like mayonnaise, so they have bread crumbs in them. Stick to the condiments that are in squirt bottles like oil & vinegar. We noticed this and asked them to hold the mayo, but if you are not careful they may put some on your sandwich without realizing they have created cross contamination.
Jimmy John's does not have gluten free bread for sandwiches, but you can order a sandwich wrapped in lettuce called an 'unwich'