The Proper Orthogonal Decomposition (POD) is a widely used method to curtail the number of degrees of freedom in parametric problems that require multiple model evaluations. Like any a posteriori reduced-order model, POD is based on extracting information of a precomputed training set, which consists of family of full-order solutions (snapshots) representative of all potential outcomes of the problem. However, in many cases, obtaining a representative collection of snapshots is computationally unaffordable. To address this challenge, we propose a data augmentation strategy, specifically formulated for the incompressible Navier-Stokes equations. The goal is to enhance the POD approximation by enriching the training set with artificial snapshots. The generation of artificial snapshots involves a combination of the original snapshots, following concepts introduced in [1], and a consideration of the physics of the problem. In particular, we exploit the incompressibility of the solutions and consider the linearised momentum balance through the solution of the Oseen equation. The new generated snapshots capture features of the parametric solutions that are not present in the original training set, thereby leading to more accurate reduced-order approximations. The strategy is applied to examples of steady-state laminar flows, in which it demonstrates superior performance compared to the standard POD. [1] P. Díez, A. Muixí, S. Zlotnik and A. García-González, Nonlinear dimensionality reduction for parametric problems: a kernel Proper Orthogonal Decomposition (kPOD), Int. J. Num. Meth. Engng, 122(24), pp. 7306--7327, 2021.