Bring a large pot of salted water to a boil over high heat. Add the pasta and cook for 6 minutes, stirring occasionally. Add the broccoli into the pasta water and continue cooking until the pasta is tender but still firm to the bite, and the broccoli is blanched, about 2 to 3 minutes. Drain pasta and broccoli, reserving 1 cup of the cooking liquid.
Meanwhile, in a large, heavy skillet heat the olive oil over medium heat. Add the garlic, red pepper flakes, salt and pepper and saute for 3 minutes. Add the clams, mussels, and wine. Cook for 5 minutes, making sure all the shells have opened. Discard any shells that remain closed. Sprinkle with the parsley.
In a large bowl, toss together the pasta, broccoli, and shellfish. Add the reserved pasta water, 1/4 cup at a time, to moisten. Toss to combine. Transfer to a serving platter and serve immediately.