Preheat oven to 425 degrees. Cook the chicken on a foil lined baking sheet for 20-25 minutes until the juices run clear. Set aside until cool enough to handle, then shred with your hands.
Heat 2 T olive oil in a large pot or dutch oven. Add the veggies and cook about 5 minutes until the onions are translucent and the other veggies are tender crisp.
Sprinkle in 1 T flour, and cook for another minute.
Add the chicken stock, buffalo sauce, and shredded chicken. Bring to a boil, and simmer 10 minutes. Stir occasionally.
Add the cheeses and stir until melted. Stir in heavy cream. Taste and add additional salt if needed.
To serve, top with blue cheese, green onions and cilantro.