Bring a large pot of salted water to a boil. Add the pasta and cook as the label directs. Reserve 1 cup cooking water, then drain.
Meanwhile, heat the olive oil in a large nonstick skillet over medium-high heat. Add the shrimp in a single layer and season with 1/4 teaspoon red pepper flakes and a pinch of salt. Cook until just pink, about 2 minutes, then flip and cook until no longer translucent,1 to 2 more minutes. Transfer to a plate.
Add the shallot to the skillet and cook, stirring with a wooden spoon, until translucent, about 2 minutes. Add the wine and cook, scraping up any browned bits, until slightly reduced, about 1 minute. Add the tomatoes, half of the basil, the remaining 1/4 teaspoon red pepper flakes and 1/4 teaspoon salt; cook until slightly thickened, about 5 minutes. Stir in the heavy cream and cook 1 more minute.
Return the shrimp and any collected juices to the skillet. Stir in the pasta; add enough of the reserved pasta cooking water to loosen the sauce. Season with salt. Top with the remaining basil.