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This paper provides a unified combinatorial framework to study orbits in certain affine flag varieties via the associated Bruhat-Tits buildings. We first formulate, for arbitrary affine buildings, the notion of a chimney retraction. This simultaneously generalizes the two well-known notions of retractions in affine buildings: retractions from chambers at infinity and retractions from alcoves. We then present a recursive formula for computing the images of certain minimal galleries in the building under chimney retractions, using purely combinatorial tools associated to the underlying affine Weyl group. Finally, for Bruhat-Tits buildings in the function field case, we relate these retractions and their effect on minimal galleries to double coset intersections in the corresponding affine flag variety., 40 pages, 7 figures best viewed in color; v3: results on double cosets restricted to function fields; final version to appear in Transform. Groups