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