Yes, just as your diet can affect your skin, your baby's diet can affect theirs.
Having healthy skin is dependent on an adequate supply of a variety of key nutrients. If you're nursing, this will come from your breastmilk, and if you're formula-feeding, this should come from the formula.
Atopic dermatitis, or what is commonly called eczema, can be triggered by diet, which can look like dryness, explains Leslie Solomonian, a naturopathic physician and associate professor at the Canadian College of Naturopathic Medicine.
If you're concerned about a specific food affecting your baby's skin, or if you're generally concerned about their skin despite getting the right nutrition, speak with your pediatrician.