Place flour into a resealable plastic bag and sprinkle with seasoning. Place 1 chicken breast at a time into bag, seal and shake to coat. Remove each breast, let sit for about 5 minutes, then place in bag, seal and shake again to coat well.
Heat oil in a large skillet over medium high heat. Add chicken and fry until golden brown and juices run clear. Transfer chicken to a 9x13 inch baking dish.
Preheat oven to 350 degrees F (175 degrees C).
In same skillet saute mushrooms and onions in pan drippings; cook, stirring, until slightly tender. Stir in broth and wine, reduce heat to medium low and simmer for 10 minutes, stirring occasionally. Pour over chicken, cover baking dish and bake in preheated oven for 30 minutes.
Mix together mozzarella and Parmesan cheeses and sprinkle mixture over chicken. Increase oven temperature to 450 degrees F (230 degrees C) and bake until cheese is melted and golden brown, 5 to 7 minutes.