What kind of oils are gluten free?

Vegetable oils. All commercial vegetable oils from large companies are heat pressed and contain no protein so are gluten free.
Oils are gluten-free. Oils are gluten-free, unless they were contaminated with gluten protein, from contact with such items as wheat, barley, malt, or rye products, during the preparation or presentation of the oils before dining. Pure oils should not have protein in them, and gluten is a type of protein.