Well, I'm sure there are foods for babies without milk and soy. Also, BRATTY is only an example of "OK foods" in diarrhea. There are many products from corn and other cereals.
The boy would need testing for common allergies.
Beside allergies this is possible:
- lactose intolerance - rare in babies but possible. Not only dairy products but anything containing lactose would affect him. Lactose is even in some medications, vitamins...
- fructose malabsorption: any fruit product or anything containing fructose, HFCS or sorbitol would affect him. Maybe even wheat. Fructose or sorbitol are aften in children syrups. Read here:
http://www.medhelp.org/user_journals/show/21247?personal_page_id=801
If nothing of above helps, he will need to be treated by experienced pediatric dietitian that can find a cause with elimination diet.