Season the chicken with salt and pepper. Add the flour to a pie plate and season with salt and pepper, paprika, and cayenne, whisking to incorporate. Dredge the chicken through the flour, shaking off the excess.
Heat a large skillet with the vegetable oil over medium-high heat. Add the chicken skin side (meaty side) down and sear until golden brown and crisp, about 3 minutes, Flip and continue cooking the other side for 3 more minutes. Remove to a platter and set aside.
Add the white wine to the skillet and scrape the browned bits from the bottom of the pan. Add the chicken stock, orange juice and zest and the hot sauce. Add the red pepper flakes and whisk in the hot sauce and mustard. Bring to a simmer and add the chicken and the juices that are left in the platter. Top with the prunes. Reduce the heat to low and cover tightly with a lid. Let the chicken braise for 40 minutes.
Uncover the chicken and remove to a serving platter. Turn the heat to high and let the sauce reduce for 2 to 3 minutes. Once thickened, taste for seasoning, and pour the sauce and prunes over the chicken. Serve immediately.