Dryness of the hands and feet since birth is uncommon. This may be due to an underlying condition like ichthyosis where there is a defect in the skin's natural moisturiser production, resulting in skin dryness and peeling.
Hand and feet eczema and other conditions like keratolysis exfoliativa and palmoplantar keratoderma can also cause dry and scaly hands and feet.
The general advice is to minimize contact with soap and detergents and irritants which can aggravate the hand dryness. Frequent application of moisturizers to improve the skin barrier is important. Topical steroids may be helpful if there is redness and inflammation of the hands.
If this is still persistent, you may consider seeing a dermatologist to confirm the diagnosis and exclude other causes. Sometimes, oral medications like methorexate and acitretin can be consider in resistent cases.