Are food allergies genetic?

Somewhat: Having allergies is genetic. Specific allergies whether to foods or inhalled allergens (like pollens, pets dust and molds) do have some familial patterns but they are not typically identical in family members, .

Loaded Question: To some degree they may be. For example in peanut allergic children subsequent sibs are probably at a higher risk than the general population for peanut allergy. However, the genetics of allergic disease is very complex and one generally passes on the ability to be allergic rather than a specific allergy.