Place flour, milk, butter, honey, egg, potato flakes, yeast, milk, salt, vanilla extract, cinnamon, and baking powder in a bread machine in the order listed by the manufacturer. Run Dough cycle. Remove dough from the machine after the cycle is done, about 1 hour 45 minutes.
Refrigerate dough until cool, about 1 hour.
Transfer dough to a bowl of a stand mixer with a paddle attachment; mix in cinnamon chips using the dough hook.
Place dough in a round pie plate; let rise until about doubled in volume, 1 to 2 hours.
Preheat oven to 375 degrees F (190 degrees C). Cover dough loosely with a tent of aluminum foil.
Bake in the preheated oven until an instant-read thermometer inserted into the center reads 175 degrees F (80 degrees C), 40 to 50 minutes.