For the capers: In a saucepot, bring the oil to a low boil. Drain the capers, and then carefully add them to the hot oil. Fry until the capers "flower," or blow out in the center, about 1 minute. Drain and reserve.
For the chevre: In the bowl of a stand mixer fitted with a paddle attachment, whip the goat cheese on medium-low speed until the cheese achieves the consistency of frosting. Add in the thyme, pepper, salt and zest, and mix on low speed until fully incorporated.
For the flatbread: Preheat the oven to 350 degrees F. Scrape any excess fat from the back of the chicken skin with a paring knife. Cut the skin into 2-inch pieces. On a parchment-paper-lined baking sheet, arrange the skins in a single layer and sprinkle with salt and pepper. Top with another layer of parchment paper and then another baking sheet to keep the skin flat while cooking. Bake until the skins are golden and crisp, rotating once while baking, 40 to 50 minutes.
To assemble, preheat the grill. Grill the flatbread about 2 minutes per side, turning 45 degrees halfway through each side to make crosshatch grill marks.
Once grilled, spread 1/4 cup chevre over surface of the flatbread, and reserve the remaining chevre for another use. Arrange the slices of speck ham over the top. Continue layering with the chicken skins, sliced pear, fried capers, chervil and lemon zest.
Garnish with a drizzle of honey, and then slice the flatbread like a pizza into 8 pieces. Serve immediately.