Scrub the clams under cold running water, then place them in a bowl and cover with a few inches of cold water. Add 1 Tbsp salt and swirl with your hands to dissolve. Let sit for 30 minutes at room temperature.
Rinse the clams in a colander under cold water. Discard any open clams that don’t close when tapped.
In a large, heavy pot with a lid, combine the clams and wine. Cover and cook over medium-high heat, shaking the pot occasionally, until the clams open, 6 to 8 minutes. Remove from the heat, uncover, and let sit until cool enough to handle, 5 minutes.
Using a teaspoon, remove the clams from their shells to a medium bowl, leaving a few clams in the shells for garnish. Discard any clams that didn’t open during cooking. Strain the cooking liquid through a paper-towel-lined sieve, into a bowl.
Rinse and dry the pot, then add 2 tablespoons of the butter and melt over medium heat. Add the garlic and pepper flakes and cook until fragrant, about 30 seconds. Add the clams, including the ones in shells, and the strained cooking liquid. Bring to a simmer. Add 3/4 teaspoon salt, 1/4 teaspoon pepper, the zucchini noodles, the remaining 2 tablespoons butter, and the 2 tablespoons parsley. Increase the heat to high, stirring, until the zoodles are somewhat tender, about 1 minute. Season to taste with salt and pepper. Distribute among 2 shallow bowls, garnish with parsley, and serve.