Demazure crystal structure for flagged reverse plane partitions

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