  Given a skew shape $ \lambda / \mu $ and a flag $\Phi,$ we show that the set
of all flagged reverse plane partitions of shape $\lambda / \mu$ and flag
$\Phi$ is a disjoint union of Demazure crystals (up to isomorphism). As a
result, the flagged dual stable Grothendieck polynomial $
g_{\lambda/\mu}(X_\Phi)$ is shown to be key positive.
