AllergyFree chicken tenders? They're available at a few different places. Those places also have a dedicated allergy-free fryer for chips (fries). They have allergy-friendly buns at a few places too, so hamburgers may be an option. I know my cousin eats the turkey legs - so that may be worth investigating (I'm not sure about wheat in the seasoning, as she's only PN/egg/dairy). I know many kids who enjoy pasta and sauce, macaroni and daiya cheese, steak, chicken, salad, gumbo (again, check the ingredients), etc.
You can get an idea of safe foods available by looking at these lists. You will have to cross-reference them for multiple allergies because I don't have links to the multiple allergy lists other than PN/TN and vegan. Otherwise, any sit-down place can accommodate top-8 allergens, but be sure to note them on your reservation ahead of time. (Otherwise it may take a long time to make something off-menu.)
peanut-free
http://wdw.wdpromedia.com/media/kana/sd/WDW-peanutFree.pdf egg-free
http://wdw.wdpromedia.com/media/kana/sd/WDW-eggFree.pdf dairy-free
http://wdw.wdpromedia.com/media/kana/sd/WDW-dairyFree.pdf wheat-free
http://wdw.wdpromedia.com/media/kana/sd/WDW-wheatFree.pdfThose are all updated regularly, so the links will still have current sheets in the future. These are specialty ingredients they have access to
in addition to their regular menu items - some of which may be safe already or easily modified with Tinkyada pasta or another ingredient on these lists. Menus can be found at
http://allears.net/dining/menu (These may not be 100% current, but will give you a general idea of what's available.)
We've also had curry at EPCOT's Rose and Crown that was free of your allergens. Sunshine Seasons food court in EPCOT's Land Pavillion has oodles of allergy-safe options they can prepare in the back to keep them safe from cross-contamination. They have a great selection of treats too. Animal Kingdom has a kiosk with allergy-friendly treats too. Fresh fruit is also widely available.
You should be able to find something safe in each park, quick serve or sit down. Have a fun vacation!!
Random other trivia - the World SHowcase restaurants in EPCOT are NOT owned by Disney and not always recommended for people with allergies due to their different allergy protocols. However, we've had great success at the UK's Rose and Crown and I have heard great reviews of Canada's Le Cellier. (I cannot speak for the other World Showcase restaurants, but allergy reviews can be found at
http://www.allergyfreemouse.com)