Pre-heat oven to 350 degrees and line a baking sheet with foil.
In a medium skillet over medium-high heat, add 1 Tbsp olive oil. Add onion to skillet and cook until softened, about 6 minutes. Add garlic and cook for another minutes. Remove onions and garlic to a medium bowl.
Add remaining Tbsp olive to same skillet and place chicken in skillet. Cook until chicken is no longer pink and is turning golden on the outside, 8-10 minutes. Remove from skillet to cutting board and let cool slightly before shredding.
In the bowl with the onion and garlic, add chicken, spinach, ricotta, feta, parmesan, parsley, one of the egg whites, salt, pepper, and red chili flakes. Mix well to combine.
Break dough into 6 equal-sized pieces and on a lightly floured surface, form each piece into an oval.
Break remaining egg white into a small bowl and, using a pastry brush, lightly brush the edges of each dough oval with egg white. Place a scoop of the chicken/spinach mixture in the middle of the dough.
Fold the dough over, pressing edges together. Crimp edges with a fork and place on prepared baking sheet.
Bake the calzone for about 15-20 minutes, until they’re brown and crispy-looking