Simulating the flow in a multi-scale media with many obstacles, such as nuclear reactor cores, is very challenging. Indeed, to capture the finest scales of the flow, one needs to use a very fine mesh, which often leads to intractable simulations due to the lack of computational resources. To overcome this limitation, various multi-scale methods have been developed in the literature to attempt to resolve scales below the coarse mesh scale. In this contribution, we focus on the Multi-scale Finite Element Method (MsFEM). An enriched non-conforming Multi-scale Finite Element Method (MsFEM) to solve viscous incompressible flow problems in heterogeneous media was proposed in [Q. Feng, G. Allaire, and P. Omnes, Multiscale Model. Simul., 20(1):462–492, 2022] . The main feature of this MsFEM is the consideration of high-order sets of weighting functions: for the velocity, they are polynomials of order n on the faces and of order n-1 in the volume of the elements; for the pressure they are polynomials of order n in the element volume. In the present work, the first error estimate for this MsFEM is obtained, proving its convergence for the Stokes problem in periodic perforated media, based on homogenization of the Stokes problem and usual Finite Element theory. In addition, it has been shown in the previously cited reference, that the continuous local problems involved in this MsFEM are well-posed. Here, their discrete counterparts are also proved to be well-posed, for any n in two dimensions and for n equal to 1 and 2 in three dimensions, with a judicious choice of non-conforming pairs of finite elements. At the numerical level, we implement the MsFEM (for n=1 and n=2) to solve the Stokes and the Oseen problems, in two and three dimensions, in a massively parallel framework in FreeFEM. The perspective of this work is to be able to solve the Navier-Stokes equations in a perforated domain at high Reynolds number using MsFEM basis functions.