Heat oven to 400°F. Place silicone baking mat on each of 2 cookie sheets or line each with parchment paper.
In 10-inch skillet, heat 1 tablespoon oil and the butter over medium-high heat. Add onion; stir to coat. Cook about 5 minutes or until onion begins to soften. Reduce heat to medium; sprinkle with salt and stir in sugar. Cook until onion just begins to brown; stir again. Continue to cook 15 minutes longer. Cool.
Meanwhile, cut pizza crust dough in 2 pieces. Roll out each as thin as possible. Place each on cookie sheet. Brush crusts with 2 tablespoons olive oil; sprinkle with salt and pepper.
Bake 5 to 7 minutes or just until crusts begin to brown but are not completely baked.
Remove crusts from oven. Spread each with 2 tablespoons peach preserves. Layer with caramelized onion, bacon and dried figs. Sprinkle with goat cheese; top with fresh figs.
Bake 5 to 10 minutes longer being careful not to over bake crust. Cut each flatbread into 4 rows by 2 rows.