Disney says
Two Angus 1/3 lb Chuck Patties with Cheese, Grilled Onions, Pickles, and our Signature- Sauce on an Allergy-friendly Bun, served with Cuties® Mandarin Oranges or French Fries.
Friendliest.app says
The Double Cheeseburger is served on an allergy-friendly bun. It is free of gluten/wheat, fish, shellfish, peanuts, tree nuts and soy.

French fries are cooked in a dedicated fryer to reduce cross-contamination.

This meal contains milk (cheese), eggs (bun) and soy (fries). It can be made milk-friendly by omitting the cheese and soy-friendly by selecting mandarin oranges instead of French fries. 

If ordered with a standard bun this meal is egg-friendly, but contains other allergens. The optional Signature Sauce contains gluten/wheat, milk, eggs and soy.