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Folks who have a problem with wheat are sometimes also gluten intolerant. It means all the cakes, donuts and other things we like will kill us
Read labels - even in health food stores. "No Gluten" = wheat free.
Other flours are rye, oat, corn, rice and graham. A grist mill like the one in Rogers, Arkansas can grind pure flour with no additives, colorants, or bleach from the natural grain. The question is whether or not there will be trace amounts of wheat flour. They can and will tell you in advance.
I cannot post a URL. Open Google. Put "Arkansas and War Eagle Mil" - without the quotes - in the search box. Press the Enter or Return key on your keyboard.
PS: Natural wheat flour is brown. It is bleached to provide the white color and then the vitamins, etc.. are added for long shelf life and other reasons.
The same thing can be said for sugar. Pure cane sugar is bleached white Molasses is added to sell you brown sugar. Buy a bottle of Brer Rabbit and make your own. Do not use sorghum.