You will find some more info in the Sea World subforum here.
We went there last spring, and my son has food allergies (dairy and egg). We did not do the all-day dining, since we just went for a couple hours at a time (had free preferred parking so we parked right near the entrance, which is so much quicker than Disney parks). I thought it was a lot, since my daughter and I can share a sandwich and be full.
Compared to Disney, they aren't quite as food allergy conscious. But, we did do fine, as far as he could get something wherever we chose to eat. I always asked to talk to someone before we ordered so they could check ingredients. They made a few adjustments to sandwiches, so then when we knew what he could get, he had the same sandwich a few times. I do think Disney is the best for allergies, though, so it's hard to compare anyone to them! At Disney they bring out a chef (or manager at counter service) every time, and make him whatever they can. They are amazing, and even though I spend more there, it is so worth it.
If you're really worried, I would pack a small cooler, making sure it's well cooled with ice packs (you could pick up some small ones at Target or
Walmart, or take them room temp in your suitcase). I don't recall, but they probably have lockers to store it in, or if you park in preferred parking you could leave it in the car and go get it later. I used to take him food everywhere, and at least at Disney would bring safe snacks (little kids like snacks) so am used to bringing a small cooler around!