Rinse and drain shrimp. Set a 10- to 12-inch nonstick frying pan over high heat; when hot, add 1 teaspoon peanut oil and the shrimp. Stir until shrimp are barely opaque but still moist-looking in center of thickest part (cut to test), 2 to 4 minutes. Pour into a large bowl.
Return pan to heat; when hot, add remaining 2 teaspoons peanut oil and the peanuts. Stir until peanuts are lightly browned, 1 to 2 minutes. Stir in chili flakes and remove from heat. Add vinegar, soy sauce, sesame oil, and sugar, and stir until sugar is dissolved. Pour over shrimp.
Add spinach and carrot to shrimp and mix gently. Mound salad equally on plates.