Place the bacon in a large, deep skillet, and cook over medium-high heat, turning occasionally, until evenly browned, about 10 minutes. Drain the bacon slices on a paper towel-lined plate. Crumble when cool; set bacon aside.

Preheat oven to 350 degrees F (175 degrees C). Spray a 7x11-inch baking dish with cooking spray.

Melt the butter in a large skillet over medium heat, and pan-fry the chicken breast halves until brown on both sides, about 6 minutes per side (meat will still be pink inside). Arrange the chicken breasts in the baking dish, and scatter the mushrooms over the chicken. Cook the green onions in the hot skillet over medium heat until softened, about 3 minutes; stir in paprika and flour. Fry the flour mixture for about 1 minute. Mash the bouillon cube in 1/4 cup of hot water in a small bowl, and whisk the bouillon into the flour mixture. Bring to a boil (sauce will be thick). Gradually whisk white wine into the skillet, and bring to a simmer. Stir the sour cream into the sauce. Pour the sauce over the chicken breasts in the baking dish.

Cover the baking dish with foil, and bake in the preheated oven for 1 hour.

About half an hour before chicken is done, bring the rice and 4 cups of water to a boil in a saucepan over high heat. Reduce heat to medium-low, cover, and simmer until the rice is tender and the liquid has been absorbed, 20 to 25 minutes. Let rice stand covered for about 10 minutes.

To serve, spoon the cooked rice onto a serving platter, and top with the chicken breasts. Stir remaining sauce in the dish, and spoon over the chicken; garnish with crumbled bacon and slivered almonds.