As with many food hypersensitivity reactions, the diagnosis of wheat allergy is challenging and often involves the exclusion of other conditions alongside carefully monitored exclusion and reintroduction of offending foods.
IgE mediated wheat allergy
Clinicians are faced with reported wheat/gluten related intolerances on a regular basis, with little evidence about the usefulness of current skin prick tests (SPT) and specific IgE tests in the diagnostic work-up of IgE mediated wheat allergy. Skin prick tests and/or specific IgE tests alongside a good clinical history or food challenge are used as the mainstay for the diagnosis of wheat allergy. However, a number of studies have recently been published on the diagnostic usefulness of component resolved diagnostics in the diagnosis of wheat allergy, indicating that these may be useful tests  in distinguishing those with true wheat allergy.
Non-IgE mediated wheat allergy
The diagnosis of non-IgE mediated wheat allergy is more complex with a lack of any validated test. The only way of diagnosing non-IgE mediated wheat allergy is to avoid the offending food (usually for a period of between 2-6 weeks) and reintroduce at home depending on the underlying pathology and severity of past reactions.
Mäkelä MJ, Eriksson C, Kotaniemi-Syrjänen A, Palosuo K, Marsh J, Borres M, Kuitunen M, Pelkonen AS. Wheat allergy in children - new tools for diagnostics. Clin Exp Allergy. 2014 Nov;44(11):1420-30.