Bring a large pot of well-salted water to a boil. Cook pasta according to package directions.
When the pasta has just 30 seconds remaining, stir in shrimp and mustard greens. Cook until shrimp are opaque and greens are vibrant. Drain, reserving 1 cup pasta water, and return everything to pot.
Stir in anchovies, lemon zest and juice, and oil. Slowly add pasta water to desired consistency. Season with salt and red chili flakes.