Flow matching has shown strong promise as a continuous generative framework, but its standard formulation is not well-suited to reasoning problems. Conventional flow matching trains a model to transport noise directly toward a single final target. For tasks that require multi-step reasoning, this direct path is often too difficult: the final answer may be reachable only through a sequence of intermediate computations or transformations. Inspired by how autoregressive language models address this challenge through chain-of-thought supervision, we introduce ReasonFlow, a framework that brings the same scaffolding principle to flow matching. Instead of supervising the flow with only a final target, ReasonFlow constructs a sequence of CoT-induced anchor points derived from intermediate reasoning prefixes. During training, the clean target moves along a piecewise-linear path through these anchors before endpoint answer readout. This turns reasoning supervision from an output sequence into a trajectory-shaping signal for flow matching. Across arithmetic, chemistry, and logical-reasoning tasks, ReasonFlow substantially improves over no-CoT flow-matching baselines.