Bring 4 quarts water to a boil in a large pot. Meanwhile, combine garlic, pepper flakes and oil in a small microwave-safe bowl and microwave until garlic is golden and fragrant, about 1 minute.
Pat chicken dry with paper towels and cut into bite-size pieces. Season with salt and pepper. Transfer 1 tablespoon of the garlic/red pepper oil to a large skillet and heat over medium heat until oil is rippling. Add chicken and cook until well browned and cooked through. Transfer to a plate and tent with foil.
Add 1 tablespoon salt and the pasta to boiling water and cook until tender but still slightly firm (al dente). Reserve 1/2 cup cooking water. Drain pasta and return to the pot. Stir in chicken, spinach, basil, lemon juice, Parmesan, and remaining garlic mixture, adding reserved pasta water as needed. Season with salt and pepper. Serve immediately.
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