Heat vegetable oil in a large pan or skillet over medium heat; saute onion, garlic, and red pepper flakes until garlic is slightly browned, 2 to 3 minutes. Add shrimp; cook and stir until shrimp begin to firm, about 5 minutes.
Stir tomatoes, peanut butter, and red chile paste into shrimp mixture; bring to a boil. Reduce heat and simmer until sauce thickens, about 20 minutes.
Place noodles in a large bowl and cover with hot water. Set aside until noodles are softened, about 15 minutes. Drain and rinse thoroughly.
Divide noodles among serving plates; top with shrimp sauce. Garnish each serving with cilantro, yogurt, and peanuts.