Soak clams in cold salted water for about 1 hour. Drain.
Bring a large pot of lightly salted water to a boil. Cook spaghetti in the boiling water, stirring occasionally, until tender yet firm to the bite, about 12 minutes. Drain.
While spaghetti is cooking, heat olive oil in a skillet and cook garlic for about 1 minute. Remove from the skillet. Add white wine and clams and cover. Cook until clams open, about 2 minutes. Remove clams from pot. Remove from shells, making sure to catch the liquid. Stir in zucchini and zucchini blossoms; season with salt and red pepper flakes and pour in clam juice. Cook until zucchini are soft, 7 to 10 minutes. When zucchini are almost soft, add clams and heat for 1 minute. Add drained spaghetti and parsley. Season with pepper.
