you can use a bakingsoda mixture, applecider vinegar, and bentonite clay. All 3 are used in place of shampoo's and are used successfully to treat flaky scalp, ringworm, eczema, scalp psoriasis successfully because they are antifungal, antibacterial, and are gentle effective clarifiers.
bakingsoda: 1/3 cup of conditioner, 4 oz of water. Pour into applicator bottle.
acv: 1:1 of acv to water. Pour into applicator bottle.
Bentonite: 1 cup bentonite clay, 2 cups water, 1 tbspn honey, 1 tbspn EVOO. Pour into empty liquid shower soap bottle.