In a small bowl, combine flour, salt and pepper; add chicken pieces and toss to coat.
Heat 1 teaspoon olive oil in a large nonstick skillet over medium-high heat. Add chicken and cook, turning occasionally, until lightly browned and cooked through, about 6 minutes; remove to a plate.
Heat remaining teaspoon oil in same skillet over medium high heat. Add peppers, mushrooms and onions, and cook for approximately 5 minutes, until tender.
Add the garlic and sauté until fragrant, about 30 seconds. Stir in tomato sauce and water; bring to a simmer over medium-high heat, scrapping up browned bits from bottom of the pan.
Return the chicken to the skillet and heat through. Remove from heat and crumble goat cheese over the top.