Bring a large pot of salted water to a boil; cook linguine in boiling water until nearly tender, 6 to 8 minutes. Drain.
Melt 2 tablespoons butter with 2 tablespoons olive oil in a large skillet over medium heat. Cook and stir shallots, garlic, and red pepper flakes in the hot butter and oil until shallots are translucent, 3 to 4 minutes. Season shrimp with kosher salt and black pepper; add to the skillet and cook until pink, stirring occasionally, 2 to 3 minutes. Remove shrimp from skillet and keep warm.
Pour white wine and lemon juice into skillet and bring to a boil while scraping the browned bits of food off of the bottom of the skillet with a wooden spoon. Melt 2 tablespoons butter in skillet, stir 2 tablespoons olive oil into butter mixture, and bring to a simmer. Toss linguine, shrimp, and parsley in the butter mixture until coated; season with salt and black pepper. Drizzle with 1 teaspoon olive oil to serve.