Final answer:
All of the given food allergies could place the client at risk for a reaction when administering an influenza vaccine.
Step-by-step explanation:
A nurse should be cautious when administering an influenza vaccine to an adult client with food allergies. Of the given options, peanuts, milk, shellfish, and eggs are all potential food allergens. However, since the question asks which food allergy could place the client at risk for a reaction, any of the given options could potentially cause a reaction in the client.