Place a large cast-iron skillet over medium-high heat. Add vegetable oil and heat until shimmering.
Carefully place the brats in the skillet and cook, turning occasionally, until browned on all sides, 6 to 8 minutes. Add apple juice and reduce heat to medium-low. Cover the skillet and cook until the sausages are cooked through, about 10 minutes more. Remove the sausages and set aside, leaving any cooking liquids in the skillet.
Add the onions and cook, stirring occasionally, until they have softened and browned slightly, about 5 minutes. Add the coleslaw mix, apple cider vinegar, caraway seeds and red pepper flakes, then season with salt and pepper and stir to combine. Cook, stirring occasionally, until the coleslaw is wilted, about 5 minutes more. Stir in the sliced apples and let cook until warmed through, another 2 minutes.
Return the cooked sausages to the skillet and serve.