  In this paper, we introduce a simple local flux recovery for $\mathcal{Q}_k$
finite element of a scalar coefficient diffusion equation on quadtree meshes,
with no restriction on the irregularities of hanging nodes. The construction
requires no specific ad hoc tweaking for hanging nodes on $l$-irregular ($l\geq
2$) meshes thanks to the adoption of virtual element families. The rectangular
elements with hanging nodes are treated as polygons as in the flux recovery
context. An efficient a posteriori error estimator is then constructed based on
the recovered flux, and its reliability is proved under common assumptions,
both of which are further verified in numerics.
