The original covering was animal skin, but canvas has been used a long time, and synthetic fabrics play an important part in the current skin boat revival. Skin boats resist generalization. Such boats are responsive in ways that their hardshelled counterparts are not, especially in absorbing wave action. This flexibility is not inherent for all skin boats, but must come from how the frame members are sized and joined. No more Beareded seal, Walrus, Sea lion etc.
People use a wide variety of fibers, but cotton canvas, nylon and polyester are the big three.
Animal skins were waterproofed with fat or oil, and needed to be dried every few days, or they got weaker and would rot. This was the biggest drawback to the original skin boats. Modern fabrics sidestep this entire issue. They are waterproofed with hypalon, urethane rubber and similar scary chemical brews. Usually has excellent hand.