Preheat oven to 350 degrees F (175 degrees C). Grease 1 baking sheet.
Whisk sorghum flour, millet flour, tapioca starch, baking powder, xanthan gum, baking soda, and salt together in a large bowl. Cut in butter with a pastry blender or 2 knives until there are no large pieces left.
Mix milk, egg, and vinegar together in a small bowl. Pour over flour and butter mixture; stir until dough comes together.
Dust a flat work surface with rice flour. Roll dough out to 1/2-inch thickness; cut into 15 biscuits with a biscuit cutter. Arrange biscuits on the baking sheet.
Bake in the preheated oven until the tops are golden brown, 15 to 20 minutes.