Boil salted water and cook the pasta for 1 minute less than the time indicated on the package. When the pasta is finished cooking, reserve ¼ cup (60 ml) of pasta water.
Meanwhile, heat two tablespoons of olive oil in a cast-iron skillet. Season cubed chicken with salt and pepper, add it to the skillet, and brown it on each side. Once cooked through — about 2 to 4 minutes — remove from skillet and reserve.
Heat remaining three tablespoons of olive oil in skillet and add garlic and red pepper flakes. Cook until fragrant, about 1 minutes.
Add kale, lemon zest, lemon juice, salt, and reserved pasta water. Cook until kale is tender, about 3 minutes.
Add cooked chicken, and pasta. Stir to coat, and serve immediately.