Mix together the flour, salt, pepper, and garlic powder in a shallow bowl. Press the chicken breasts into the flour mixture to coat well. Set the coated chicken breasts aside on waxed paper; do not stack.
Melt the butter in a skillet over medium heat, and cook and stir the mushrooms with 1/4 cup of the wine until the mushroom juices have been absorbed and the mushrooms are beginning to brown, about 15 minutes. Push the mushrooms to the edge of the skillet and place the coated chicken breasts into the center of the pan. Brown the chicken breasts on each side, about 5 minutes per side, and pour in the remaining 1 cup of wine. Cover the pan, and cook until the chicken is no longer pink inside, about 10 minutes.
Remove the chicken breasts from the pan, and arrange on a warmed serving platter. Pour the cream into the skillet, bring to a boil over medium heat, and cook, stirring frequently, until the brown flavor bits on the bottom of the skillet have dissolved and the sauce has thickened, about 10 minutes. Pour the sauce over the chicken, and serve.