Allure is quite relaxed with the dress suggestions. Men get in on formal nights with slacks and a dress shirt with no tie or jacket. Our son likes to wear a suit though, so he is well within the suggested dress. The lines between casual and smart casual have become quite blurry and from my observations on several Royal Caribbean ships they have both come to mean simply 'casual' with virtually nobody wearing a jacket or tie on 'smart casual' nights, even though their dress code still has the jacket and tie listed. For better or worse, the truth is the dining room management doesn't want to endure the hassle of confronting guests as long as they are reasonably attired and not looking sloppy.
The above is even more true if you opt for My Time Dining since the ambience is akin to a land-based restaurant with people constantly coming and going.
So, my advice is to not spend a lot of money on new clothes for your son. Some Docker-style pants, a dress shirt, and some Izod style golf shirts will suffice. As for footwear, athletic shoes are fine. Just leave the flip flops in the cabin if going to dinner.