In a large, cast-iron or stainless steel skillet over medium heat, heat 1 Tbsp. oil. Add onion; season with ½ tsp. salt. Cook, stirring occasionally, until onions start to soften, about 6 minutes. Add bell pepper and jalapeño and cook, stirring occasionally, until starting to soften, about 5 minutes. Add garlic and cook, stirring, until fragrant, about 1 minute more.
Push onion mixture to edges of pan. Pour in remaining 1 Tbsp. oil, then add chicken; season with 1 tsp. salt. Cook, breaking up chicken into small pieces, until browned, about 5 minutes. Add tomatoes and chili powder; season with pepper. Increase heat to high and bring to a simmer. Cook, stirring occasionally, until slightly thickened, 3 to 4 minutes.
Reduce heat to medium and stir in BBQ sauce. Bring to a simmer and cook, stirring occasionally, until sauce is thickened, about 5 minutes; season with salt and pepper, if needed. Remove from heat.
In a large bowl, toss cabbage, carrot, scallion, mayonnaise, cilantro, vinegar, sugar, and ¾ tsp. salt.
Spoon chicken mixture onto cut sides of bottom buns. Top with coleslaw and dill pickles, then close with top buns.