Dissolve sugar and yeast in 3/4 cup warm water in a small bowl; let stand 5 minutes.
Weigh or lightly spoon flours, flaxseed meal, and potato starch into dry measuring cups; level with a knife. Combine flours, flaxseed meal, potato starch, xanthan gum, and salt in a medium bowl; beat with a mixer at medium speed until blended. Add yeast mixture, 1/4 cup olive oil, and 2 eggs; beat at medium speed 1 minute or until blended.
Turn dough out onto a lightly floured surface; divide dough into 8 equal portions. Shape each portion into a ball. Coat dough balls with cooking spray; place on a baking sheet. Cover with plastic wrap, and let rise in a warm place (85°), free from drafts, 1 hour and 15 minutes, or until almost doubled in size.
Combine 1/2 cup boiling water and tomatoes in a bowl; let stand 10 minutes or until soft. Drain and chop.
Heat a Dutch oven over medium-high heat. Add 2 teaspoons oil; swirl. Add onion and garlic; cook until onions is golden brown, stirring often. Add tomatoes; cook 1 minute. Place onion mixture in a bowl.
Add spinach to Dutch oven, stirring until spinach wilts. Place spinach in a colander, pressing until barely moist. Add spinach, cheeses, oregano, 1/4 teaspoon salt, and pepper to onion mixture, stirring to combine. Divide mixture into 8 equal mounds.
Preheat oven to 425°.
Working with 1 portion at a time, place dough on a floured surface. Pat into a 6-inch circle. Spoon 1/4 cup spinach mixture onto dough circle. Fold dough over filling; pinch edges to seal. Repeat procedure with remaining dough and filling. Place calzones on a baking sheet coated with cooking spray. Combine 1 tablespoon water and 1 egg in a small bowl, stirring with a whisk until frothy. Brush egg mixture over calzones. Bake at 425° for 25 minutes or until golden brown.
Gluten-Free Baking; The Food Lover's Gluten-Free Cookbook