Bring a large pot of water to a boil and liberally season with salt. Add the pasta and cook according to the package directions until al dente. Drain, reserving 1/4 cup of the cooking water.
While the pasta cooks, heat a 12-inch nonstick skillet over medium heat. Heat the butter and olive oil until the butter melts. Add the zucchini and cook, stirring, until golden brown, 5 to 6 minutes. Add the corn and garlic and cook, stirring occasionally, until the corn has softened, about 5 minutes. Season with salt and pepper and reduce the heat to low.
Add the pasta, squash blossoms and chopped basil to the skillet. Stir together, adding the reserved cooking water, if the mixture looks too dry. Add the feta and stir through. Taste for seasoning and add more salt or pepper, if needed.
Scoop into a large shallow bowl and garnish with basil leaves. Serve warm or at room temperature.