Sprinkle the chicken thighs with salt and pepper and then melt the coconut oil in a large skillet set over high heat. When the pan is hot enough, add the pieces of chicken, nice-looking side down, and cook them without moving them for about 4 minutes, until they turn opaque about halfway up and develop a nice golden crust. Flip the pieces of chicken and cook them for another 3 to 4 minutes, until the meat is cooked all the way through, and the juices run clear. Remove to a plate.
Put the skillet back over the heat source, lower the heat to medium and add the broccoli. Cook it for about 3 minutes, until slightly softened.
Meanwhile, mix the chicken stock, vinegar, mustard, chili pepper flakes and tapioca starch together in a large glass measuring cup or other container, preferably one that is equipped with a spout.
Pour this over the broccoli as soon as it’s cooked to your liking; bring to the boil and continue cooking until the sauce thickens, about 2 minutes.
Add the chicken thighs, along with their cooking juices, back into the pan and spoon some sauce over them.
Kill the heat, cover and allow the meat to sit in the hot sauce for about 5 minutes, then serve.