Place beans in a bowl; cover with plenty of water. Soak for 8 hours or overnight.
Drain beans and transfer to a large pot; cover with plenty of water, salt, and 1/4 teaspoon cayenne pepper. Bring to a boil, reduce heat, and simmer until beans are soft, about 90 minutes. Drain and season with salt.
Grind walnuts and garlic to a fine paste in a food processor. Add vinegar, 1/3 cup water, 1 tablespoon parsley, 1 tablespoon cilantro, and 1/4 teaspoon cayenne pepper. Process until smooth.
Mix beans, onion, chicken, and dressing in a bowl. Chill in refrigerator for at least 1 hour before serving. Garnish with 1 tablespoon parsley and 2 tablespoons cilantro.