Rinse quinoa. Bring 4 cups of salter water to a boil and add quinoa. Cook covered for 15 minutes. Let stand for 5 minutes, covered, and transfer to a bowl to cool.
Heat olive oil in a large sauté pan. Add chopped leeks and sauté with salt and pepper until soft but not brown. Add zucchini and sauté for about 2 minutes. Add spinach and let wilt. Allow vegetable mixture to cool.
Combine quinoa and vegetable mixture together in a large mixing bowl. Add eggs, goat cheese, cayenne, and chili flakes. Combine thoroughly. Season with salt and pepper to taste.
Fill a quarter cup measurement with quinoa mixture. Place upside down on a lined baking sheet to form patty shape (the same way you may build a sand castle!). If the quinoa is not sliding out easily, rinse the measuring cup with water between each patty. Continue until all patties are formed.
Bake for about 40 minutes at 400 degrees, or until brown and crispy.