Everyone seems to have different sensitivity so my experience may be different from yours. I have been trying to avoid foods with nickel for about 2 years now. I try to use common lists on foods to avoid and have challenged some foods that I just do not want to give up. Most of the time I find that I loose the challenge. What I am trying to imply is that I can tell when I eat a food that is high in nickel, at least in my own sensitivity range.
In regards to wheat, the information that I read states that whole wheat (and whole grains in general) are high in nickel, but processed (white) wheat is OK. That would imply that there is a higher concentration of nickel in the husks or germ of many grains (my own assumption). I do not limit white flour (pizza crust and white bread included) in my own diet and have not found an issue. I have not thought about the mill and getting nickel from stainless steel parts. I would think that stainless steel would be a poor material for the part of the mill that would actually grind the grain. I would suspect that an industrial mill would have something harder for the grinding teeth, tungsten carbide or a minimum of hardened steel (which would not contain large amount of nickel). The “stone ground” label on the flour is probably more of a marketing term than anything. (Tungsten carbide is a ceramic so would you consider that a stone?).
I worry more about liquids, especially acidic ones in contact with metals. I try to avoid products packaged in metal cans, especially acidic ones like tomato sauce and have abandoned my stainless coffee mug.
I do not eat whole wheat products, but have not challenged them yet. I may as my wife is prefers whole wheat products and is pushing me to try.
I do get blindsided by things that are not listed anywhere occasionally. Beware of ginger and gingerale it took me a while to figure out that the burn in my throat that I felt when drinking gingerale was not normal…. Winter squash (pumpkins and spaghetti squash) also got me as well as pomegranates.
I hope this helps. These allergies seem to be a personal thing, my tolerance to nickel will be different than your son’s. To make things even worse, most people are allergic to more than 1 thing. I think 3 things were average for people suffering from esonophillic esophagitus (a condition caused by an allergic reaction). Myself I am also allergic to beef and some pollen that is high in late winter and early spring.
Hang in there, I do miss may foods that I can no longer eat, but after an initial drop in weight, I have found plenty of things to eat and loosing weight has not been a problem.