Heat oil in a large pan over medium heat. Add in the onions, green peppers, celery, and garlic. Saute until vegetables are tender, about 15 minutes, stir often.
In a small bowl, whisk together the flour and water until smooth, set aside.
Stir into the pan of vegetables, the tomatoes with juice, parsley, salt, pepper, flour mixture, and okra. Bring to a boil, reduce heat, cover, and simmer until okra is tender, about 15 minutes, stir often.