Bring the water and chicken broth to a boil in a large pot or Dutch oven. Add the chicken, potatoes, carrots and celery and reduce heat to a simmer. Cover the pot and simmer for 25-30 minutes until chicken is cooked through and easy to shred. Remove the cooked chicken breasts to a plate and shred with two forks. Replace the lid and continue to simmer the rest.

Mix together the flour, salt and pepper in a bowl until combined. In a medium saucepan, melt the butter over medium heat. Stir in flour a spoonful at a time to smoothly combine with the butter. Pour the half and half in a little at a time, stirring continuously with a whisk to allow the roux to combine with the cream. Continue whisking and adding half and half until the mixture is smooth and creamy. Add the cheddar and blue cheeses and stir in. Continue to cook, stirring occasionally for a few minutes until the cheeses are melted in and well combined. Add in the wing sauce and stir to combine.

Add the shredded chicken and the Buffalo sauce mixture into the soup pot and stir to combine. Bring back to a simmer and simmer for 10 minutes or so to allow the soup to thicken and the flavors to combine.