Heat a tablespoon of olive oil in the frying pan, add onion and cook until lightly brown. Add minced garlic, chili flakes, salt and pepper, shredded chicken and 2/3 cup of enchilada sauce. Mix well and simmer for 10 minutes.
Cut zucchini into thin slices using vegetable peeler. Arrange 4 slices on a cutting board with the edges overlapping. Put 2 tablespoons of chicken mixture, roll up and transfer to the greased baking dish. Repeat with the remaining zucchini slices and chicken mixture.
Pour the remaining enchilada sauce over the rolls and top with shredded cheeses.
Bake at 350F for 20 minutes. Serve topped with full-fat yogurt and chopped parsley.