In a large pot of salted boiling water, cook linguine according to the package directions until al dente. Drain, reserving ½ cup pasta water, and return to pot. In a large skillet over medium heat, heat oil. Add shrimp and season with salt and pepper. Cook until shrimp is pink and cooked through, 4 minutes. Remove from skillet and reserve on a plate. Add butter to skillet then add garlic and red pepper flakes and cook until fragrant, 1 minute. Add tomatoes to skillet and cook until beginning to soften, 3 minutes. Season with salt and pepper. Add wine and cook until mostly reduced, 5 minutes.
Add heavy cream, lemon juice, and Parmesan. Let simmer until sauce is thickened, 5 minutes. Add pasta, shrimp, and kale and toss to coat. If sauce is too thick, add additional pasta water.
