Bring a large pot of salted water to a boil. Cook the spaghetti according to the package instructions until al dente. Reserve 1 cup of the pasta water before draining.
In a large skillet over medium heat, warm the olive oil. Add the garlic and red pepper flakes. Stir and cook for 30 seconds to 1 minute, or until the garlic is lightly browned at the edges. Add the kale, salt, and several grinds of black pepper, tossing with tongs until the kale is wilted, about 1 minute.
Add the cooked spaghetti to the skillet and toss to combine. Pour in ½ cup of the reserved pasta water, lemon juice, and lemon zest, and toss everything together. If the pasta seems too dry, add more pasta water to create a light sauce.
Adjust seasoning to taste. Garnish with chopped parsley and serve with Parmesan or vegan Parmesan.