Cook bacon in a Dutch oven over medium- high heat until crisp. Remove bacon from pan; crumble and set aside
Add onion, carrot, and garlic to pan; cook, stirring constantly, 5 minutes. Add potato, chicken, salt, pepper, and 4 cups milk; bring to a boil. Cover, reduce heat to medium, and simmer 20 minutes or until potatoes are tender, stirring occasionally.
Place flour in a small bowl; gradually add remaining 1/4 cup milk, stirring until smooth. Add flour mixture to chicken mixture. Bring to a boil over medium-high heat. Reduce heat, and simmer, uncovered, 5 minutes, stirring frequently.
Add corn and 1 cup shredded cheese to chicken mixture; stir until cheese melts. Divide mixture evenly among 9 bowls; top with crumbled bacon and remaining 1/2 cup shredded cheese.