In a skillet, warm the olive oil and sauté the onion until golden. Stir in the garlic, chili flakes, salt, pepper, shredded chicken, and 2/3 cup of enchilada sauce. Cook for 10 minutes.
Slice the zucchini thinly with a vegetable peeler. Lay 4 slices on a board, overlapping them. Place 2 tablespoons of the chicken mixture on top, roll it up, and place in a greased baking dish. Repeat with the remaining ingredients.
Pour the leftover enchilada sauce over the rolls and sprinkle with cheese.
Bake in a preheated oven at 350°F (175°C) for 20 minutes. Serve with full-fat Greek yogurt and chopped parsley on top.