1. In a 6- to 8-quart pan over high heat, bring about 4 quarts water to a boil; add linguine and cook, stirring occasionally, just until tender to bite, 6 to 8 minutes. Drain pasta, reserving about 1/3 cup cooking liquid; return pasta to pan.
2. Meanwhile, in a 10- to 12-inch frying pan over medium-high heat, melt butter with olive oil. Add shrimp, garlic, chili flakes, pepper, and 1/4 teaspoon salt; stir for 2 minutes. Add wine; stir often until shrimp are opaque but still moist-looking in center of thickest part (cut to test), 3 to 4 minutes longer. Stir in basil.
3. Pour shrimp mixture into pan with cooked pasta; mix gently. If mixture is too dry, add reserved pasta-cooking liquid. Divide evenly among four wide, shallow bowls. Add salt to taste.