Place navy beans into a Dutch oven with 8 cups water; bring to a boil. Boil for 2 minutes, then remove from the heat. Cover and let stand until beans are softened, about 5 hours.

Drain beans and discard soaking liquid. Rinse beans and return to the Dutch oven. Add ham hocks, chicken broth, remaining 4 cups water, onion, parsley, garlic powder, basil, black pepper, oregano, nutmeg, and bay leaves. Bring soup to a boil, then reduce the heat and simmer until beans are tender, about 1 1/2 hours.

Stir carrots, celery, and potato flakes into soup until well combined. Cover and simmer until vegetables are tender, about 30 minutes more.

Transfer ham hocks to a cutting board. When cool enough to handle, remove meat from the bones and cut into bite-sized pieces. Return meat to the pot and warm through over medium heat, about 3 minutes.