Add in the onion, celery, and garlic; stir/saute until tender, about 5 minutes.
Add in the stock and potatoes; bring to a boil; decrease heat to medium-low and simmer, covered, until the potatoes are tender, about 20 minutes; stir in the corn.
In a medium bowl or pitcher, whisk together the flour and 1 cup of the milk; add the remaining milk and blend; stir into the soup, increase heat to med-high, and stir until slightly thickened, 3-5 minutes.
Decrease heat to med-low and add the chicken, tomato, salt, and pepper to taste; simmer, uncovered, until the flavors are blended, about 10 minutes.
Remove pot from the heat, add in the cheese, and stir until melted (do not boil after the cheese is added).