Preheat the oven to 350°. Lightly brush the flat breads on both sides with olive oil. Toast them directly on the oven rack for 6 minutes, or until golden.
Brush the jalapeños lightly with olive oil. Roast them over a gas flame or under the broiler until softened and blackened in spots, about 4 minutes. Transfer the jalapeños to a bowl, cover with plastic and let cool. Peel, seed and cut the jalapeños into thin strips.
Spread the Taleggio on the breads, leaving a 1-inch border all around. Top 4 of the breads with the jalapeño strips, 4 with the artichoke hearts and 4 with a mix of the olives and almonds.
Just before serving, bake the flat breads directly on the oven racks for 5 minutes, or until crisp on the bottom and the cheese is melted. Cut into wedges and serve.
Make Ahead: The flat breads can be prepared through Step 3 earlier in the day and refrigerated.