Cut each chicken thigh into quarters (or 1 1/2-inch pieces, if large). Pat dry and season with 1 teaspoon salt. Heat the vegetable oil in a large skillet over medium-high heat. Add the sausage and cook, stirring, 1 minute. Add the chicken in a single layer and cook undisturbed until browned, about 4 minutes. Continue to cook, stirring occasionally, until the chicken is golden brown all over, about 5 more minutes. Sprinkle the flour over the chicken and cook, stirring, 1 minute.
Stir in the broth and potatoes and bring to a boil. Reduce the heat and simmer, covered, until the potatoes are just tender, about 10 minutes. Stir in the okra and cook, covered, until the chicken and potatoes are cooked through, 5 to 10 more minutes. Remove from the heat and stir in the lime juice and cilantro.