Preheat the oven to 375°F.
In a large bowl, mash the spinach, goat cheese, and sun-dried tomatoes with a fork until it holds together when pressed. Season with a big pinch of salt and set aside.
In a small bowl, combine the basil, garlic powder, oregano, 1 teaspoon salt, black pepper, and red pepper flakes (if using). Pat the chicken dry with a paper towel and season all over with the spice mixture.
Starting on the fat end of the breast, carefully cut a 3-inch-long horizontal slit to create a big pocket without slicing the chicken in half. Evenly spoon the goat cheese mixture into each pocket. Press down firmly on the top to seal.
Heat the oil in a large cast-iron or ovenproof skillet over medium heat. Add the chicken and cook until golden brown on each side, 3 to 4 minutes per side. Immediately transfer the skillet to the oven.
Bake until the chicken reaches an internal temperature of 165°F, 14 to 16 minutes.
To serve, slice the breasts on an angle and fan one breast on each plate.
