Preheat the oven to 400°F. Line a baking sheet with parchment paper.
In a large bowl, combine the ground chicken, breadcrumbs, Parmesan cheese, parsley, onion, garlic, oregano, salt, black pepper, red pepper flakes (if using), and egg. Mix until well combined.
Using your hands, form the mixture into meatballs, about 1 to 1.5 inches in diameter. Place the meatballs on the prepared baking sheet.
Drizzle the olive oil over the meatballs. Bake in the preheated oven for 20-25 minutes, or until the meatballs are cooked through and golden brown.
While the meatballs are baking, prepare the tzatziki sauce. In a medium bowl, combine the Greek yogurt, grated cucumber, garlic, olive oil, lemon juice, salt, and pepper. Mix well and refrigerate until ready to serve.
Once the meatballs are done, remove them from the oven and let them cool slightly before serving with the tzatziki sauce.