There is a difference between contact and biting induced cheilitis. Contact ceilitis is indicated by swelling. The lips would increase in size as part of the bodies histamine response. As is seen in bee stings, and allergic reactions to i.e. botox injections, there is considerable increase in size from swelling. The pictures of the OP indicate nothing of this nature. It's not a reaction to wheat. There are no links between exfoliative cheilitis and wheat allergies. If a wheat allergy were the cause it would show elsewhere in skin rashes/itching, dermatitis/ Psoriasis etc, not just mild flaking of the upper epidermis of the lips. You cannot be certain this is the cause and there are no examples that I can find where a person has cured their EC from excluding wheat. I have personally tried it with no success.
Most of the people I've seen on here developed EC either from accutane, overuse of Antibiotics , or lip biting (due to dehydration which may or may not have an underlying cause) or a combination of all these. I would think the one thing most people here have in common above all else is an emotional vulnerability/hypersensitivity which results in nervous behavioural patterns like lip biting.