Preheat an outdoor grill for medium-high heat and lightly oil the grate. Spread butter, 1 tablespoon salt, 1 tablespoon pepper, and garlic powder over chicken breasts on a plate or cutting board.
Grill the chicken breasts until no longer pink in the center and the juices run clear, 5 to 6 minutes per side. An instant-read thermometer inserted into the center should read at least 165 degrees F (74 degrees C).
Bring a large pot of lightly salted water to a boil; add penne and cook, stirring occasionally, until tender yet firm to the bite, about 11 minutes. Pour penne into a colander to drain.
Place the penne, chicken breasts, spinach, 1/2 cup Parmesan cheese, and red pepper flakes in the pot. Cook and stir over low heat until the spinach is wilted but still green, about 7 minutes. Season with the remaining 1/2 cup Parmesan cheese, salt, and pepper.
Mix pasta into spinach-chicken mixture; toss well.