Preheat your oven to 400°F. Place the flatbreads on a baking sheet.
In a small bowl, mix together the olive oil, honey, balsamic vinegar, thyme, salt, and pepper. Brush this mixture evenly over the flatbreads.
Sprinkle the crumbled goat cheese over the flatbreads, followed by the fresh blueberries.
Bake in the preheated oven for 12-15 minutes, or until the flatbreads are golden and the cheese is slightly melted.
Remove from the oven and let cool for a couple of minutes. If desired, top with fresh arugula before slicing and serving.