Bring a large pot of lightly salted water to a boil. Add pasta and cook for 8 to 10 minutes or until al dente; drain.
Meanwhile heat olive oil in a large frypan over medium-high heat. Add onions, garlic and chilli flakes. Cook and stir until the onion has softened and begun to turn golden brown, about 5 minutes. Stir in capers, anchovies and diced tomatoes then bring to a simmer. Stir in kale and simmer over medium-low heat until wilted and tender, about 10 minutes.
Once the pasta has cooked and been drained, stir into the sauce along with the black olives. Toss and sprinkle with grated Parmesan cheese before serving.