In a large bowl, whisk together gluten free flour, sugar, instant yeast, xanthan gum, and salt. Add warm water, olive oil, and egg. Mix until a soft dough forms. Cover and let rise in a warm spot for 30 minutes.
While dough rises, prepare the filling by mixing ricotta, mozzarella, parmesan, chopped spinach, garlic, red pepper flakes, salt, and pepper together in a bowl.
Preheat oven to 400F and line a baking sheet with parchment paper. Divide dough into 4 equal pieces. On a sheet of parchment paper dusted with gluten free flour, pat each piece into a 7-inch round.
Place about 1/3 cup of filling on one half of each round, leaving a 1/2-inch border. Fold the dough over the filling and press the edges firmly to seal, then crimp with a fork. Place on the baking sheet and cut 2 small slits on top of each calzone.
Brush tops with olive oil and bake for 20 to 22 minutes until golden brown. Let cool 5 minutes and serve with warm marinara sauce.