Heat olive oil in a large pot over medium heat.
Add the chicken breasts and season with salt and pepper.
Stir in minced garlic and red pepper flakes, cooking until fragrant.
Pour in the chicken broth, scraping the bottom of the pot to deglaze.
Bring the broth to a simmer and add in the spaghetti.
Cook the spaghetti, stirring occasionally until al dente, about 8-10 minutes.
Stir in the heavy cream, lemon zest, and juice.
Add the spinach and allow it to wilt in the pot.
Taste and adjust seasoning with salt and pepper as needed.
Serve hot, garnished with fresh parsley.