What is the average time a person can have an allergic reaction?

Variable. This is highly variable depending on the allergic reaction. Major reactions can occur immediately up to 8 hours after the fact. Minor reactions can have a delayed hypersensitivity occurring 24-72 hours later.
Minutes to hours. The onset of allergic reactions is usually rapid, within minutes of exposure to the allergen. The latest start to an allergic reaction is perhaps one to two hours. Allergic reactions will usually last anywhere from 30 minutes to several hours, though longer reactions are sometimes possible. Reactions outside these time parameters are probably not "true" allergies but other kinds of intolerance.