Disney says
Double Beef Patty Slider on an Allergy-friendly Bun, served with Cuties® Mandarin, Yogurt Smoothie and choice of small Lowfat Milk or small DASANI® Water. Meets Disney Nutrition Guidelines for Complete Meals without substitutions
Friendliest.app says
The Double Basecamp Burger can be served on an allergy-friendly bun that is free of gluten/wheat, dairy/milk, fish, shellfish, peanuts, tree nuts and soy.

This meal contains eggs (bun) and is not listed as soy-friendly. It can be made milk/dairy-friendly by omitting the Dannon Danimals smoothie and selecting water instead of milk. 

If ordered with a standard bun, this meal is egg-friendly, but contains other allergens.