All sugar cookies are based on some type of flour, but you can make them without using white flour. There are several recipes available online that substitute finely ground almond meal or rice flour for the traditional white flour that is normally used.
Anyone who suffers from celiac disease is normally required to follow a gluten-free diet, which excludes most types of wheat, barley and rye, including white flour, farina, semolina flour and spelt. Rice grain is allowed, making rice flour a popular substitute for white flour in gluten-free cooking. When making flourless sugar cookies, simply substitute an allowable ground meal or rice flour for the white flour, and then use the eggs, sugar and flavorings as required.