Place kidney beans in large pot. Add enough water to pot to cover beans by 2 inches. Bring to boil. Remove pot from heat. Cover and let beans stand 1 hour to soften. Drain. Return beans to same pot. Add 7 cups water and chicken broth. Bring to boil. Reduce heat to medium-low and simmer until beans are tender, about 1 hour. Drain beans, reserving 2 cups of cooking liquid.
Heat vegetable oil in heavy large skillet over medium-high heat. Add 2 cups onions and saute' until beginning to soften, about 4 minutes. Add sausage, bell pepper, celery, and garlic. Reduce heat to medium and saute' until vegetables are tender, about 10 minutes. Stir in beans, reserved 2 cups cooking liquid, 1 teaspoon salt, 1/2 teaspoon black pepper, paprika, and cayenne. Reduce heat to low; simmer until liquid thickens slightly, about 15 minutes.
Meanwhile, combine remaining 2 3/4 cups water, rice, butter, bay leaf, thyme, and remaining 1/2 cup chopped onion, 1 teaspoon salt and 1/4 teaspoon black pepper in a large saucepan. Bring to simmer over high heat. Cover, reduce heat to low and cook until rice is tender and water is absorbed, about 20 minutes. Remove from heat and let stand covered 10 minutes.
Spoon kidney beans into bowls. Top with rice and serve.