Many things can affect the results of food allergy testing–including eczema.
In individuals with severe eczema they may not be able to tolerate a skin prick test as they may develop a skin reaction from the actual test and not the allergen. For example if your skin swells easily to minor scratches, the skin prick test might not be a reliable test for you.
Eczema can also increase your total IGE levels potentially affecting your blood test results. While it is not common, there have been cases where some individuals with extremely high scores to an allergen are not actually allergic. The high scores are due to high total IGE levels related in part to extreme eczema.
If you think you might not be allergic to an allergen or have accidentally ingested an allergen without reaction–you should discuss this with your allergist.