Flaxseed oil is rich in short chain omega-3s: these are inefficiently converted in the human body to the useable long chain format (DHA and EPA) at rates as low as 10%. Furthermore short chain omega-3s are much less stable than long chain omega-3s so the oil easily oxidises and goes rancid.
GrahamPhillips is correct that flaxseed oil is more processed than extra virgin olive oil or virgin avocado oil: not least because olives and avocados (both fruits) are soft and easily cold-pressed, whereas flaxseeds have a hard, indigestible coating so need to be finely ground to release the oil.
The only rich dietary source of long chain omega-3s are oily fish (eg. mackerel/ sardines/ salmon/ trout). Oily fish are also the only rich dietary source of bioavailable vitamin D. UK healthy eating guidelines recommend up to four servings of oily fish each week. There is no minimum requirement for flaxseeds or their oil, it simply is not essential for health.
There are much smaller amounts of omega-3s (DHA and EPA) and vitamin D3 in organic, free-range eggs from hens fed a seed rich diet. Dr Mosley’s advice on extra virgin olive oil and oily fish are on pages 103 to 110 of the Clever Guts Diet book.
Please do not use dietary supplements – including oils – without the guidance of a qualified health professional (eg. family doctor, registered dietician) who has access to your medical notes and/ or your detailed food and symptom diary.