In a large heavy pot, preheat the oil to medium/high heat for a few minutes. Whisk flour into hot oil, reduce heat and continue whisking often until the roux turns a deep brown, about 10-12 minutes. Season the chicken with the Creole or Cajun spices and set aside. When the roux is ready, add the onions and stir with a wooden spoon, cook for another 10 minutes.
Add chicken pieces to the roux and cook for the next 6 to 8 minutes, turning as needed. Add the smoked sausage and cook for a minute. Add the celery, poblano, bell pepper, jalapeño, tomato, garlic, thyme, bay leaves, and chicken broth. Bring to a boil, reduce heat and cook for 45 minutes.
In a small bowl, add the 2 tablespoons of flour, add the 4 tablespoons of cold water and whisk until smooth, to make a slurry. Add the slurry to the gumbo and stir well to combine. Add in the Spanish chorizo or andouille sausage, chayote(or zucchini), and Worcestershire sauce. Season to taste with salt, pepper, and hot sauce. Cook for another 20 minutes. Remove bay leaves and thyme and serve over rice. Garnish with chives and parsely.