Bring a large pot of salted water to a boil. Add the linguine and cook as the label directs. Reserve 1 cup cooking water, then drain.
Meanwhile, season the shrimp with salt. Heat the olive oil in a large skillet over medium-high heat. Add the garlic and red pepper flakes and cook until the garlic is just golden, 30 seconds to 1 minute. Add the shrimp and cook, stirring occasionally, until pink and just cooked through, 1 to 2 minutes per side. Remove the shrimp to a plate. Add the wine and lemon juice to the skillet and simmer until slightly reduced 2 minutes.
Return the shrimp and any juices from the plate to the skillet along with the linguine, butter, and 1/2 cup of the reserved cooking water. Continue to cook, tossing, until the butter is melted and the shrimp is hot, about 2 minutes, adding more of the reserved cooking water as needed. Season with salt; stir in the parsley. Serve with lemon wedges.