Cook the bacon over medium heat in a large soup pot. Remove bacon from the pot and place it on a paper towel to drain.
Add the onion, celery, and fresh thyme to the soup pot; cook 3–4 minutes until softened.
Whisk the milk and flour together; add to the pot. Add the chicken broth and potatoes, and bring the mixture to a boil, stirring frequently. Reduce the heat to low, cover the pot, and simmer until the potatoes are cooked through and the soup is thickened, about 15 minutes.
Chop the bacon.
Add the corn and cook 5 minutes. Stir in the crab, cilantro, lime juice, salt, and bacon; cook 2 minutes until heated through. Serve with crackers or flatbread, if desired.