Your veterinarian will perform a full physical exam on your cat. This will allow her to take a proper look at his symptoms and rule out possible causes of his condition based on his symptoms. She will also collect a verbal history from you. She will want to know when his symptoms started, if they have been progressing, if you have been trying to treat at home with over the counter products and so on. All these details can help the veterinarian with her diagnosis.
Naturally, the veterinarian will need to rule out other possible causes of his symptoms such as gastrointestinal parasites or flea bite hypersensitivity. These things can also cause the skin and gastrointestinal symptoms so your veterinarian may run some basic diagnostic testing to rule out other suspected issues. If you want to rule out environmental allergies, there is a blood serum test you can pursue if desired.
Unfortunately, there is no serum, blood, or intradermal test reliable for diagnosing food allergies. The main way to come to a proper diagnosis is a trial and error dietary study; it is known as an elimination diet trial. You remove the suspected food item from his diet for a minimum of 12 weeks. This gives his system time to remove any remaining ingredient from his system completely and hopefully his symptoms will begin to resolve. Gastrointestinal signs typically resolve between 1 to 3 weeks. Dermatologic symptoms take much longer to resolve as it takes the skin time to heal. If his symptoms have resolved during this time, you need to reintroduce the suspected food item to get a confirmation. If you offer the Greenie product to your cat again and his symptoms reappear almost immediately, you have your culprit.