Preheat oven to 375°F. Whisk eggs, milk, salt, and pepper together in a bowl and set aside.
Heat olive oil in a 10-inch oven-safe skillet over medium heat. Sauté onion for 3 minutes until softened.
Add spinach and cook, stirring, for 1 to 2 minutes until just wilted.
Pour the egg mixture over the vegetables. Scatter feta and red pepper flakes evenly on top.
Cook on the stovetop for 2 minutes until the edges start to set, then transfer to the oven.
Bake for 12 to 15 minutes until the center is fully set. Slice into wedges and serve warm.