The use of essential oils such as tea tree, lavender, and chamomile can be very beneficial when it comes to treating dryness and eczema on the head. Tea tree oil relieves inflammation and lessens flakiness due to its antifungal and anti-inflammatory properties. Chamomile oil with its mild properties soothes and moisturizes the scalp, while lavender oil reduces irritation and inflammation. You can use these essential oils to relieve dryness and eczema on the scalp by diluting them in a carrier oil, such as coconut or jojoba oil, and massaging them into the scalp.