Preheat the oven to 425°F and spray a 12-cup muffin tin with nonstick cooking spray.
Combine the hash browns, salt, black pepper, red pepper flakes, and 1 cup of the cheese in a medium bowl.
Divide the potato mixture among the muffin cups and press it down and up the sides to form nests. Bake for 25 to 30 minutes, until the bottoms are browned.
Meanwhile, cook the bacon in a skillet over medium-high heat until crisp. Transfer it to paper towels to drain, then reserve a little for topping.
Remove the hash-brown cups from the oven and reduce the oven temperature to 350°F.
Whisk the eggs and milk together in a small bowl.
Melt the butter in a skillet over medium-low heat. Add the eggs and gently stir with a spatula until thickened and no liquid remains.
Fold most of the cooked bacon into the eggs.
Spoon the egg mixture into the potato cups. Top with the remaining cheese and reserved bacon.
Bake for 4 to 5 minutes, until the cheese melts. Sprinkle with chives and serve warm.