Robotic fabric manipulation remains challenging due to fabric deformability and occlusions from wrinkles and the manipulator. This paper defines Random-to-Target Fabric Flattening (RTFF) as the task of bringing a randomly wrinkled fabric to an arbitrary user-specified wrinkle-free target pose. RTFF requires simultaneous flattening and pose alignment, where the two objectives are inherently coupled since flattening the fabric displaces its pose, while realigning it tends to introduce wrinkles. To solve this task, this paper anchors both the current and target fabric states to the same template mesh, enabling direct vertex-level wrinkle and pose assessment without registration. Building on this representation, a hybrid Imitation Learning--Visual Servoing (IL--VS) RTFF policy is proposed. A novel Mesh Action Chunking Transformer (MACT) leverages structured mesh observations to achieve goal-conditioned coarse alignment from a compact demonstration set, after which VS ensures precise convergence to the target. The policy is validated on a real dual-arm teleoperation system, demonstrating precise alignment to unseen target poses, fabric types, and scales. Code and videos: https://kaitang98.github.io/RTFF_Policy/

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