Position an oven rack in the lower-middle and preheat the oven to 425°F (220°C).
Place the lavash on a rimmed baking sheet and brush both sides lightly with the olive oil.
Bake the lavash 3 to 4 minutes, until golden brown; remove from the oven and let it cool slightly on the pan.
While the lavash cools, toss the shredded chicken with the hot sauce and melted butter in a medium bowl until evenly coated.
Sprinkle the shredded Monterey Jack evenly over the cooled lavash.
Spread the buffalo chicken mixture evenly over the cheese, then sprinkle the chopped spinach on top.
Return the topped lavash to the oven and bake 4 to 6 minutes, until the cheese is melted and the chicken is heated through.
Let the flatbread cool briefly, transfer to a cutting board, cut into 8 pieces, and drizzle the blue cheese dressing over the slices before serving.