Heat oil in a large Dutch oven over medium-high heat. Add chicken; cook, stirring occasionally, until browned all over, 8 to 10 minutes.
Stir in bell peppers, onion and garlic; cook, stirring often, until softened, about 4 minutes. Add paprika, salt and hot paprika; cook, stirring constantly, until fragrant, about 1 minute. Add tomatoes, scraping the bottom of the pot to loosen browned bits. Add broth; bring to a boil over high heat.
Stir in noodles; cover and reduce heat to low. Cook until the noodles are tender and the chicken is cooked through, about 8 minutes.
Stir sour cream and flour together in a small bowl until smooth. Stir into the soup. Cook, stirring occasionally, until the soup is thickened, 3 to 5 minutes. Top with parsley and serve.
