Delayed Food Allergy
"Delayed Food Allergy" does seem to be known to medical science
Treatment of delayed food allergy based on specific immunoglobulin G RAST testing.
This preliminary, descriptive study after extensive clinical experience demonstrates specific IgG food RASTs done in 114 consecutive patients with strong positive histories for delayed food allergy.
However, as Fabian points out in a comment, there are only a handful of mentions of this term in scientific papers.
A more widely used term may be Delayed Hypersensitivity or Type IV hypersensitivity.
In Allergies: Dubious
Diagnosis and Treatment on Quackwatch
it is asserted that
scientific studies have found that only about 6% of children and 1-2% of adults actually have a food allergy, and most people with food allergies are allergic to less than four foods
The correct way to assess a suspected food allergy or intolerance is to begin with a careful record of food intake and symptoms over a period of several weeks.
Proper medical evaluation—done best by an allergist—will include careful review of your history and skin testing with food extracts (using a prick or puncture technique) to see whether an allergic mechanism is involved in your symptoms.
Additional information on food allergies and food intolerance is offered from an article at Science-Based Medicine. The author is a pharmacist and the article is well-referenced. Here are a few excerpts:
When it comes to food intolerance testing, blood tests are just the start. Other methods used include vega testing, the K-Test, hair testing,and applied kinesiology. But the blood tests are enjoying new popularity... Hemocode is just one of several blood tests that’s marketed. There’s also the YorkTest in the United Kingdom and also Canada. The Hemocode is an IgG blood test. The YorkTest is also an IgG test. There is no published information in the literature that describes either the Hemocode or the Yorktest, or their analytic validity for any of the products tested for.
Food allergies are reaction to food proteins. They may be categorized as immunoglobulin E (IgE)–mediated (immediate) reactions, non–IgE-mediated (delayed) hypersensitivity reactions, and mixed reactions. IgE-mediated reactions are the ones we worry about when we hear about a “food allergy”: flushing, itchy skin, wheezing, vomiting, throat swelling, and even anaphylaxis... IgG molecules mediate interactions of cells with different cellular and humoral mechanisms. IgG antibodies signify exposure to products—not allergy. IgG may actually be a marker for food tolerance, not intolerance, some research suggests.
At present, there are no reliable and validated clinical tests for the diagnosis of food intolerance. While intolerances are non-immune by definition, IgG testing is actively promoted for diagnosis, and to guide management. These tests lack both a sound scientific rationale and evidence of effectiveness. The lack of correlation between results and actual symptoms, and the risks resulting from unnecessary food avoidance, escalate the potential for harm from this test. Further, there is no published clinical evidence to support the use of IgG tests to determine the need for vitamins or supplements. In light of the lack of clinical relevance, and the potential for harm resulting from their use, allergy and immunology organizations worldwide advise against the use of IgG testing for food intolerance.