Prepare the pasta according to the package directions, in a pot of salted boiling water, until al dente. Reserve 1 cup of the pasta cooking water before draining the pasta.
Heat the oil in a large skillet over medium heat. Add the garlic and red pepper flakes. Stir and cook 30 seconds to 1 minute, until the garlic is lightly browned around the edges. Add the kale, salt, and several grinds of pepper and cook, tossing with tongs, until the kale is wilted, up to 1 minute.
Add the spaghetti and toss to combine. Add ½ cup pasta water, lemon juice, lemon zest, and toss. If the pasta is seeming too dry, add the remaining ½ cup pasta water to create a light sauce.
Season to taste. Garnish with parsley and serve with Parmesan or vegan Parmesan.