Put the chicken pieces in a large bowl. Add enough cold water to cover the chicken. Stir in 2 tablespoons of salt. Cover and refrigerate for 4-12 hours.
Fire up your Vortex. Let the coals get just ashed over. To make gravy place small disposable aluminum pans under a few of the pieces of chicken.
Remove chicken from the brine. Do not rinse. In a pie plate or shallow bowl, combine the flour and salt and pepper to taste. Dredge the chicken pieces in the flour, coating completely. Shake off any excess.
Transfer the chicken to the grill around the Vortex. Cover and cook 45 minutes, rotating the lid every 15 minutes. Check for near doneness (160 F for white meat, 170 F for dark meat) in several places before removing.
Lightly brush the chicken with oil and cook another 2-3 minutes to crisp the skin and finish cooking the chicken (165 F for white meat, 175 F for dark). Remove to a plate or cooling rack.