The choice of oil for a liver-flush should ideally be high quality oil that doesn't contain any chemical additives. Oils are often cloudy making them appear unappealing and oxidise quickly giving then a short shelf life; consequently they are clarified and preserved by the manufacturers with chemicals. High quality cold pressed virgin olive oil doesn't oxidise easily and is a firm cost effective favourite for liver flushing. This does not preclude the use of other oils and all oils are digested quickly. Human fat is our natural food store and contains a high proportion of oleic fatty acid. Unsaturated fats do not require complex digestive processing and are simple broken down into their molecules (micro-emulsification) and then simple absorbed through the walls of the intestines.
Oleic fatty acid induces a pancreatic secretion of protein enzyme and, to a lesser extent, of water and bicarbonate. It would appear that oils high in mono-unsaturated Oleic fatty acid are very suited to liver flushing because of their rapid transit and absorbs ion in the gut.
Macadamia is a good alternative and flaxseed oil has also been used successfully. I am sure sesame and peanut oil have been used although they are strong oils. Avocado oil looks very suitable but I have read any reports about it. Canola is a good alternative and cold pressed varieties are available but it has a poor reputation because of the mass produced cooking product.