https://www.disboards.com/threads/gluten-free-dining-at-the-disneyland-resort-a-superthread.3003289/
The old list was 'stickied' at the top but it's gone now and some of the older info may be outdated but this is still a great resource. If I'm looking for something specific I usually start at the end of the thread and work backwards so I get the latest info first.
http://www.glutenfreedairyfreewdw.com/menus/
This link is to the allergy friendly menus. You'll have to scroll down thru the WDW links to find the DLR links. Again, menus change so these may not be 100% accurate.
Tell your dad he'll be great. Disney is second to none when it comes to accommodating those of us with food sensitivities. Tell him there will be GF french fries to eat with his GF burger at Smokejumpers and Hungry Bear AND that Lucky Fortune Cookery in DCA has a wonderful (gasp) GF teriyaki bowl!!!! The grilled cheese/tomato soup combo at Jolly Holiday is YUM and Plaza Inn has GF pot roast with GRAVY!!!
TS places are no problem. They have fresh ingredients and if nothing appeals then the chefs can usually whip something up for him from what's to hand. I've had some delicious 'off menu' meals created just for me. QS/CS places don't have that luxury as they usually don't have large kitchens with lots of ingredients. They can only work with adapting what's on the menu.
My usual strategy at QS/CS places is to look at the posted regular menu and try to find at least two things that look to me as if they'd be easy to convert to GF. Ask the first CM you see if they can accommodate or if they have an allergy menu (they'll usually have one to show you). If not, once I get to the order-taker I ask for the GF menu or to speak to the chef to see if either of my choices will work or to pick from what's there. If your dad has been GF for a while he'll pretty much know that it would be easy to 'convert' certain dishes (putting a burger/sandwich on a gf bun or 'hold' the sauce on a dish), and not so easy to convert others (no GF fried chicken or corn dogs, sorry).
Tell dad that there are not a lot of fresh 'snacky' things in the parks. No churros, no fresh baked goods. Plenty of packaged snacks though and popcorn and fresh fruit. Dole Whips are GF AND Sprinkles cupcakes in DTD do a very good GF cupcake. I usually throw in a few GF granola bars so I don't get 'hangry'.
Relax, don't worry, have fun. I've never been 'glutened' at Disney. And I always eat very well.
Oh, one more thing. At QS/CS places the GF meals take between 15-20 minutes longer to prepare so the non GF people are usually half done eating when I get my food. BFF and I have worked around this by having me get in line first and she gets in line about two parties behind me. This seems to coordinate OK with our food being done at about the same time. We pay separately which may have something to do with it, I don't know if they coordinate with the non GF people if you're paying on one tab. At TS, this isn't an issue.