In a large Dutch oven over medium heat, brown bacon pieces, then drain on paper towels and reserve. Add butter, onion, and celery and cook until onion is translucent. Add in garlic and cook an additional minute.
Sift flour over onion mixture, stirring to combine. Increase heat to med-high, then add potatoes, clam broth, and reserved juice from canned clams and bring to a boil for 1 minute. Reduce heat to medium-low, add in fresh thyme sprigs and bay leaves. Gently simmer until potatoes are just tender, about 20 minutes. Remove thyme and bay leaves and discard.
Add in clams, cream, and milk, heat for 3-4 minutes until warmed through (do not boil). Season will salt, pepper, pinch of cayenne.
Serve in bowls sprinkled with cooked bacon and minced chives.
Oyster crackers and crusty bread are wonderful too.