With a small, sharp knife, peel mangoes. One at a time, set fruit on one narrow edge on a board and cut 1/8-inch-thick slices off each side down to the pit. Save remaining fruit around pits for another use.
Cut peel off jicama and discard. Lay jicama on board, flattest side down, and cut into 1/8-inch-thick ovals. Trim slices, if necessary, to match size of mango slices, about 2 by 4 inches.
Pour habanero vinaigrette into a rimmed plate. Dip a jicama slice in dressing, turning to coat and letting excess drain back into plate; set jicama on a separate plate. Lay a mango slice on top (if slices aren't perfect, fit pieces together to cover). Repeat to stack a total of four jicama and four mango slices. Coat remaining jicama slices and layer with mango slices to make three more servings.
Drizzle remaining dressing equally over stacks. In a small bowl, mix cilantro with olive oil and salt and pepper to taste. Mound equally on stacks.
Habanero Vinaigrette: Rinse 1 fresh habanero chili (about 1/4 oz.). Wearing rubber gloves, stem, seed, devein, and finely mince chili; you should have about 1 1/2 tablespoons. In a small bowl, mix 2 teaspoons of the minced chili, 1/3 cup fresh orange juice, 2 tablespoons fresh lime juice, and 1 tablespoon extra-virgin olive oil. With a small, sharp knife, cut ends off 2 limes (3 oz. each); cut off peel, including white pith. Holding limes over bowl of dressing, cut between membranes and fruit to release segments and drop them into bowl. Mix gently and add salt and more chili to taste, if desired.