We propose Q-Guided Value-Gradient Matching (Q-VGM), an offline-to-online RL method for fine-tuning flow-matching vision-language-action policies with a learned critic. Directly applying critic gradients to flow policies requires backpropagation through the multi-step denoising process (BPTT), which is costly and unstable at VLA scale. Motivated by an optimal-control view of denoising, we derive a local approximation connecting clean-action value gradients to local velocity corrections at late denoising steps. Q-VGM uses this connection to construct critic-guided targets for fine-tuning the pretrained action expert through velocity matching. Gradients pass only through local velocity predictions, avoiding backpropagation through the denoising trajectory. An action-sensitive chunk critic is trained with IQL offline and TD learning online. On LIBERO, Q-VGM improves the few-shot-SFT four-suite average from 84.6% to 90.7% offline using 150 policy rollouts per suite, and reaches 98.4% after online training. Compared with on-policy RL, Q-VGM achieves 5.3x higher sample efficiency on average across four LIBERO suites, measured by the episode budget for 95% rollout success rate. On three real-world bimanual tasks, offline Q-VGM improves average success from 66.7% to 98.3%.

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