There are many wonderful carrier oils for burns that nourish the skin and speed its healing. Baobab oil, shea butter and tamanu oil are three of my current favorites.
Baobab: The oil is made by cold-pressing the seeds of the fruit of the baobab tree (Adansonia digitata). Baobab oil is highly penetrating, deeply nourishing and softens dry skin. It is known to restore and remoisturize the epidermis. Baobab oil has a high essential fatty acid content.
Shea: Shea butter is extracted from the the Karite tree (Butyrospermum parkii), most often found in the tropical regions of West Africa. Shea is an excellent moisturizer. It is used as a lip balm, salve base, in body butters and in many skin care preparations. Great for sun-damaged skin and for long-term health of the skin.
Tamanu : The oil is made from the Calophyllum inophyllum tree, but it isn't immediately present in the plant. The harvested fruits are crushed to extract the nuts. The nuts are then sun-dried for eight weeks. During this time, the nuts turn brown and lose a third of their original weight. Inside, their oil content becomes very high. Tamanu oil doesn't actually develop until this period. Once dried, the oil is extracted from the nuts by cold pressing. Tamanu oil’s ability to heal damaged skin has been well researched. The oil is notable for reducing scars, stretch marks (it fades stretch marks with great results), minor wounds, skin irritations, rashes, bed sores and many other skin concerns.