Preheat the oven; mise en place - Adjust oven rack to middle position and preheat oven to 425℉. Destem the bell pepper, remove the ribs and seeds, and chop into a medium dice. Trim and dice the celery. Peel and dice the onion. Trim the scallions and chop, separating the white and green parts. Remove the skin and trim the fat off of the chicken thighs. Slice the kielbasa. Peel and devein the shrimp.
Toast the flour - Place flour in pie plate and toast it in the preheated oven, stirring occasionally, until it begins to take on some color and tastes smoky, 30 to 40 minutes. Remove from the oven and transfer to a bowl.
Create the base and cook the chicken - Heat the oil in a Dutch oven over medium heat until shimmering. Add the bell pepper, onion, celery, whites of the scallions, and salt and pepper, and cook, stirring frequently, until softened. Add the Cajun Seasoning, and stir to coat the vegetables. Stir in 2 cups of broth. Add the chicken in single layer (chicken will not be completely submerged in liquid) and bring to a simmer. Reduce heat to medium-low, cover, and simmer until chicken is fork-tender, 15 to 17 minutes. Transfer chicken to a plate.
Build the gumbo - Slowly whisk the remaining 2 cups broth in small increments into the toasted flour until a thick, smooth paste forms. Slowly whisk the paste into gumbo, making sure each addition is incorporated before adding next. Turn up the heat to medium. Stir in the water and the sliced kielbasa. Simmer, uncovered, until the gumbo thickens slightly, 20 to 25 minutes.
Finish - Once cool enough to handle, shred the chicken into bite-size pieces. Stir the shredded chicken, shrimp, and half of the chopped scallion greens into the gumbo. Cook until the shrimp is opaque, then remove the pot from the heat, stir in vinegar, and season with salt to taste. Garnish with the rest of the scallion greens, and serve with white rice or crusty bread.