Demazure crystal structure for flagged reverse plane partitions

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