Slowly melt the butter with the liquid smoke in a saucepan over medium heat, then gradually whisk in the flour. Cook, whisking continuously, until the color is a light chocolate brown, 10 to 15 minutes. Pour the roux into a 6- to 7-quart slow cooker.
Toss the onion, bell pepper, celery and garlic in the slow cooker, then arrange the chicken on top. Sprinkle with the Cajun seasoning and file powder. Add the chicken broth, cover and cook on low, about 6 hours.
Transfer the chicken to a cutting board. Shred the meat, discarding the bones, then return the meat to the slow cooker.
Add the shrimp, cover and cook until they turn pink, about 8 minutes.
Serve over rice; top with the scallions and hot sauce.
Photograph by Ryan Liebe