Place a large pot of water over high heat. Bring to a boil and add a generous pinch of salt. Add pasta and cook to package directions for al dente, about 7 to 8 minutes.
Slice the squash and zucchini in half lengthwise. Slice each half into 1/4-inch thick "half moon" slices and set aside.
While the pasta is cooking, heat a large skillet over high heat and add 2 tablespoons olive oil. Add the zucchini, season with salt and pepper and cook 3 to 4 minutes, until slightly browned, tossing halfway through. Remove the zucchini to a plate. To the same pan, add another 2 tablespoons olive oil. Add the yellow squash, season with salt, and pepper and cook 3 to 4 minutes, until slightly browned, tossing halfway through. Remove to a plate with zucchini.
To the same skillet add the remaining olive oil and turn down heat to medium. Add the garlic and red pepper flakes and saute 1 minute. Add the tomatoes, season with salt and pepper and saute for another 2 minutes. Add the cooked squash, zucchini, herbs and goat cheese, toss together and saute 1 minute.
Strain the pasta and return to the pot. Add the sauteed vegetables to the pot and toss. Taste and adjust seasoning, if necessary. Transfer to a serving bowl, garnish with a little bit fresh basil and parsley and serve immediately.