I had stomach aches from not knowing i had celiac for 9 years. When i was on the diet i felt improvement, but still felt 70% until i took out other various food.
Obviously took out oats.
Next to gluten, potatoes were the worst
Anything really acidic (especially orange juice)
Meats that are hard to chew (seafoods gross but it didn't hurt my stomach
i'm not suggesting you take out those specific foods. Sorry, i know nothing about down syndrome, but i know something about stomach aches. Perhaps take out certain foods that you have been feeding him and try without it for a few weeks (i didn't feel improvement until it's been a long time from stopping from eatting it) Obviously check with your doctor before you do anything.