Remote-sensing foundation models increasingly unify representations across sensing modalities and downstream tasks, yet their prediction mechanisms remain largely task-specific. Separate decoders, prediction heads, and objectives leave prediction fragmented across tasks. This naturally raises a question: can heterogeneous remote-sensing tasks share the prediction process? UniFlow-RS answers this question with a single latent flow-matching predictor shared across tasks. This requires addressing two key challenges: unifying heterogeneous prediction spaces and harmonizing joint optimization across tasks. First, we cast heterogeneous task outputs into structured visual targets in a common latent space, allowing them to be modeled by the same pretrained flow predictor. Task-dependent conditioning further accommodates differences in input configurations. Second, we optimize all tasks with a common Flow Matching objective, eliminating task-specific prediction losses. To mitigate optimization mismatch across tasks and modalities, we introduce Task-Modality Adaptive Timestep Sampling (TMAS), which dynamically allocates training timesteps according to the online learning state of each task-modality group. Using a single shared model, UniFlow-RS handles six tasks and thirteen datasets, surpassing recent task-specific state-of-the-art methods on several benchmarks while remaining competitive on the others. Beyond these benchmarks, the same checkpoint demonstrates strong zero-shot transfer across unseen datasets, task settings, occlusion conditions, and near-infrared false-color imagery, without target-specific adaptation.

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