My LO is MPI, although growing out of it, and eczema is one of the symptoms for her. She drinks either oat or rice milk, both of which are very low in fat, so I add in quite a lot of coconut milk to her diet as well - either actually mixed with her milk (mmm, yummy!) or in smoothies and baking. It's hot here and she likes ice in her drinks so I had the idea recently of freezing coconut milk in ice trays and adding a cube to her cup of oat milk. I also drizzle olive oil on her bread and sometimes on meals, and she has nut butters. She also love hummus, which is homemade with plenty of olive oil in it.