Stir tomatoes, wine, chicken stock, tomato paste, and chicken bouillon together in a large bowl. Trim chicken as necessary; sprinkle with Italian herb blend.
Heat olive oil in a skillet over medium-low heat. Cook chicken breasts until browned, 3 to 5 minutes per side. Transfer chicken to slow cooker along with any accumulated juices.
Place bell peppers, onion, mushrooms, and garlic in skillet, along with more olive oil if needed. Cook and stir until onion is translucent, about 5 minutes. Stir in flour; cook until vegetables are soft, about 5 minutes.
Stir in tomato mixture; bring to a boil. Simmer until thickened slightly, about 5 minutes more. Stir in olives; transfer mixture to slow cooker.
Reduce slow cooker heat to Low and cook until chicken is very tender, 5 1/2 to 6 1/2 hours. Stir pesto and sugar into chicken mixture; cook for 30 minutes more.