Crisp bacon in a large frying pan over medium-low heat. Remove to a paper-towel-lined plate, set aside to cool, then crumble.
Discard all but 2 tablespoons of the bacon fat, add onion, and cook, stirring rarely, until well-browned, about 15 minutes. Add vinegar and cook until the strong vinegar aroma has dissipated, about 1 minute. Remove the pan from heat and let cool slightly.
Place arugula in a large nonreactive bowl. Slice figs crosswise into 1/4-inch coins and add to the bowl along with crumbled bacon and cooled onion mixture. Toss to evenly combine and season with additional vinegar, salt, and freshly ground black pepper as desired.
Evenly arrange mixture on toasted flatbread. Cut into squares and serve.