Bring a large pot of water to a boil; season well with salt. Add the pasta and stir to prevent sticking.
Meanwhile, heat a large skillet over medium-high heat. Add the oil, pepper flakes, garlic, shallots and 1/2 teaspoon salt. Cook, stirring often, for 2 minutes. Add the zucchini and yellow squash and season with 1 teaspoon salt. Toss well to coat in the flavors and cook another 3 minutes.
Using a pair of tongs, check the pasta. If it is just under al dente, it is ready to transfer. Using the tongs or a pasta fork, transfer the pasta from the water directly to the skillet with the squash and toss well to coat. Add the lemon zest and juice and 1/2 cup of the pasta water and toss well. Sprinkle with the arugula and toss to wilt slightly. Finish with the ricotta salata and a drizzle of olive oil before serving.