Do not add oil to your scalp – washing off the natural oils that Malassezia feeds on is more likely to help.
Some chemicals can help kill it off; the most effective anti-fungals are miconazole and ketokonazole. Some shampoos contain ketokonazole, but miconazole is currently only available in skin creams (and some pet shampoos!).
If you find the effects of an antifungal shampoo wear off after a while, try another product. Coal tar shampoos can slow down skin turnover (but may discolour fair hair). Shampoos containing salicylic acid can help get rid of the flakes. Shampoos containing zinc or selenium can also target the fungus.
BBC 2 Trust Me, I'm a Doctor January 2016
NHS Choices website - page on dandruff