Remove seeds and core from the red and green bell peppers, then slice them into thin strips. Chop the yellow onion finely. Cut the chicken into bite-size pieces and sprinkle with kosher salt.
Warm the vegetable oil in a large skillet over medium-high heat until hot. Add the chicken pieces, onion, bell peppers, and the taco seasoning mix. Stir frequently and cook until the vegetables soften, about 5 to 8 minutes. Rinse and drain the black beans during this time.
Pour in the black beans, diced tomatoes with their juices, instant brown rice, and chicken broth. Stir everything well and bring the mixture to a boil. Lower the heat to a simmer, cover the skillet, and cook for 8 to 10 minutes, until the chicken is done and rice is tender. Remove from heat and let it sit, covered, for another 5 minutes to soak up the remaining liquid.
Top with shredded Mexican cheese blend and add any preferred garnishes like cilantro, avocado, sour cream, or jalapeño slices before serving.