Bring a large pot of lightly salted water to a boil. Cook linguine at a boil until tender yet firm to the bite, about 11 minutes. Reserve 1 cup pasta water; drain linguine well in a colander set in the sink.

Melt 2 tablespoons butter with 1 1/2 tablespoons olive oil in a large skillet over medium heat. Add bell peppers and garlic; cook and stir until peppers have softened, about 10 minutes. Stir in shrimp; cook and stir until shrimp are opaque and pink, about 5 minutes. Transfer shrimp to a bowl and set aside, leaving peppers and garlic in the skillet.

Stir wine, clam juice, and lemon juice into the skillet; bring to a boil over medium heat. Add remaining 2 tablespoons butter and remaining 1 1/2 tablespoons olive oil; return shrimp to the skillet. Stir in reserved 1 cup pasta water, parsley, cream, pepper flakes, and salt. Add cooked linguine; toss lightly to coat. Simmer scampi over medium-low heat to let linguine absorb some sauce, about 5 minutes; serve hot.