Quantifying aleatoric uncertainty in medical image segmentation is critical since it is a reflection of the natural variability observed among expert annotators. A conventional approach is to model the segmentation distribution using the generative model, but current methods limit the expression ability of generative models. While current diffusion-based approaches have demonstrated impressive performance in approximating the data distribution, their inherent stochastic sampling process and inability to model exact densities limit their effectiveness in accurately capturing uncertainty. In contrast, our proposed method leverages conditional flow matching, a simulation-free flow-based generative model that learns an exact density, to produce highly accurate segmentation results. By guiding the flow model on the input image and sampling multiple data points, our approach synthesizes segmentation samples whose pixel-wise variance reliably reflects the underlying data distribution. This sampling strategy captures uncertainties in regions with ambiguous boundaries, offering robust quantification that mirrors inter-annotator differences. Experimental results demonstrate that our method not only achieves competitive segmentation accuracy but also generates uncertainty maps that provide deeper insights into the reliability of the segmentation outcomes. The code for this paper is freely available at https://github.com/huynhspm/Data-Uncertainty