To make the wings, stir together the lime juice, vinegar, olive oil, salt, black pepper, garlic and cayenne for a marinade. Place the wings in the marinade, and let sit unrefrigerated for 30 minutes. (If you want to marinade it longer, please keep in the refrigerator.)
Meanwhile, in a dry skillet heated on high, toast the chiles de arbol and guajillo on each side for about 10 seconds or just until they start to puff. Fill the skillet with enough water to cover chiles. Leave the heat on until water begins to boil and then turn off the heat and let the chiles soak until soft, about 30 minutes.
To cook the wings, preheat the oven to 375° F, and place a rack on a baking sheet lined with foil. (If you don’t have a rack, don’t worry—the wings will taste the same but be a little less crisp as the rack helps the fat drain as they cook.) Remove the wings from the marinade and place on the rack. Cook for 25 minutes, turn the wings over, and then cook for 20 more minutes.
While the wings are in the oven, remove the chiles from the soaking water, rinse and place in a blender. Add to the blender the garlic, cumin, oregano, allspice and 3/4 cup of water. Blend for 5 minutes until smooth. (You blend the chiles this long because they have very tough skins and this ensures the salsa is smooth without having strain it and lose some of the flavor.) In a skillet, heat up the oil on medium low and pour in the salsa. Cook for 10 minutes, stirring occasionally. Remove from heat, stir in the vinegar and add salt to taste. You can add more vinegar or water if you desire a thinner sauce.
After the wings have been in the oven for 45 minutes, remove from the oven and generously brush both sides with the red chile salsa (you can save remaining salsa for another use. It’s terrific on tacos and on eggs). Return to the oven and cook for 10 more minutes.
(Alternatively, you can cook the wings on the grill, about 10 minutes per side, turning once, brushing with sauce after removing from the grill.)
Sprinkle the jicama and radish slices with cayenne, and serve alongside wings with chipotle blue cheese dressing for dipping.
The salsa is hot so if you wish to cut down on the fire I would reduce the amount of chiles de arbor used.