Bring a large pot of salted water to a boil. Add the pasta and cook for 1 minute less than the time indicated on the package, until al dente. Reserve ¼ cup (60 ml) of the pasta cooking water, then drain.
2. Step
Meanwhile, heat 2 tablespoons of olive oil in a large cast-iron skillet over medium heat. Season the chicken with salt and pepper, then it to the skillet, until browned on each side and cooked through, 2–4 minutes. Remove from the pan and set aside.
3. Step
Heat the remaining 3 tablespoons of olive oil in the same skillet. Add the garlic and red pepper flakes and cook until fragrant, about 1 minute.
4. Step
Add the kale, reserved pasta water, lemon zest, lemon juice, and salt. Cook until the kale is tender, about 3 minutes.
5. Step
Add the chicken and pasta to the pan with the kale and toss to combine.
6. Step
Serve immediately with freshly grated Parmesan cheese on top.