Put the drumettes and chicken legs into separate shallow dishes and sprinkle with salt and pepper. Add 1/2 teaspoon red pepper flakes and 2 rosemary sprigs to each dish. Drain the pears and save the juice and pears. Reserve 2 tablespoons juice for the salad dressing. Pour the remaining juice from 1 can of pears over each dish and toss to coat evenly. Cover and refrigerate for at least 1 hour or up to overnight.
Make the dressing by whisking together the reserved 2 tablespoons pear juice, lime juice, olive oil, and salt and pepper to taste. Cover and refrigerate until ready to serve.
When you are ready to fry the chicken, heat an inch of canola oil over medium-high heat in a heavy skillet to 350 degrees F. Put the flour into a shallow dish and season it well with cayenne, salt and pepper. Remove the chicken from the marinade, reserving the marinade. Pat the chicken dry and coat with the flour mixture. Let them rest on a plate while the oil gets hot. Fry the chicken in batches. Drain them on paper towels and keep warm.
While the chicken is cooking, add the marinade to a medium pot. Pick out the rosemary sprigs, add the shallots and bring to a boil. Cook until the marinade has reduced by half, about 5 minutes. Add the pears and cook until they are hot. Pour the mixture into a blender, add the cranberry jelly and butter, and puree carefully as it is hot. Taste and adjust the seasoning with salt and pepper. The mixture should be thick but pourable. If it is too thin, put it back into the pan and reduce it a bit.
Pour some of the spicy pear sauce onto a plate and place the chicken legs or drummettes on top. Toss the arugula with the dressing and put a small pile onto each plate.