To prepare the balsamic reduction, in a small saucepan over medium-high heat, bring balsamic vinegar to a simmer. Reduce heat to medium-low, and simmer until the vinegar has reduced to 1/4 cup, about 20 minutes. Set aside and let cool.
Heat a large skillet over medium heat and add the bacon. Cook until crisp; remove bacon and crumble.
Preheat oven to 400 degrees. Place pieces of naan in a single layer on a large baking sheet. Divide goat cheese between the pieces of naan and use a spoon to spread it over the top. Sprinkle the bacon on top of the goat cheese. Layer the avocado, strawberries, and mango over the top, diving between the pieces of naan.
Bake for 10 to 15 minutes, or until the toppings are cooked and the crust is slightly golden. Remove flatbread from oven, sprinkle with basil and garnish with the balsamic vinegar reduction. Slice and serve warm.