I had a lot of food allergie and have cruised with them with no problem.
I posted a question about food allergies, on cruise critic (a long time ago). The first thing you should do is you or your TA notify Disney about the allergy. The response I got on cruise critic was that the Disney medical department would contact you via phone and then meet with when you are on the ship.
My experience (not Disney) was that I would have my TA notify the cruise line and then I would go and see the MaitreD soon after I boarded the ship. Each evening they would give me a menu for the next night, so I could order what I could eat, prepared the way I needed it. If I went to the dining room for breakfast and lunch, they would also prepare food the way I needed it. I also talk to the MatreD about the food at the buffets and he would advise me about how they were prepared.
Pancakes are usualy made with milk, but eggs are not. Also you mentioned pancakes, in the dining room I am sure they would make them without milk for you son.
I think most of the cruise lines have soy milk available, but you should ask Disney to be sure.
Hope this helps.
Sue