In a large bowl, combine the ground chicken, feta cheese, Greek yogurt, breadcrumbs, garlic, oregano, lemon juice, salt, black pepper, and red pepper flakes (if using). Mix until well combined but do not overmix.
Divide the mixture into four equal portions and shape each portion into a patty.
Preheat a grill or skillet over medium heat. Lightly grease the grill or skillet with cooking spray or a little olive oil.
Cook the patties for about 5-7 minutes on each side, or until the internal temperature reaches 165°F and the burgers are golden brown.
Toast the whole wheat burger buns on the grill or in a toaster until lightly browned.
Assemble the burgers by placing a patty on each bun, then topping with spinach leaves, tomato slices, and cucumber slices. Serve immediately.