Non-equilibrium cold atmospheric pressure plasma (CAPP) micro-jets have gained significant attention in biomedical applications, such as wound healing, cancer treatment, and sterilization. These devices ionise a noble gas jet directed towards a surface by applying high voltage, producing a non-equilibrium, low-temperature plasma flow. In the context of tumour treatment, CAPP micro-jets have demonstrated the ability to affect cancerous cells while preserving the surrounding healthy tissue, as shown in experimental studies. The role of fluid dynamics in plasma discharge behaviour is not yet fully understood. Most experimental and numerical studies operate plasma jet devices at low flow rates, corresponding to strictly laminar regimes, to maintain stable discharge conditions. However, realistic operating scenarios may involve higher Reynolds numbers, leading to turbulent jet flows. This work examines how large-scale laminar and turbulent jet flows influence the dynamics of non-equilibrium plasma plumes and the micro-scale transport of reactive ion and metastable species. An open-source plasma fluid numerical model is developed within the OpenFOAM framework, coupling macro-scale gas flow with micro-scale plasma transport equations. The solution of the compressible Navier-Stokes equations for the gas mixing is inserted as an input to the plasma equations (i.e., Poisson's and species continuity equations), which allows the estimation of the discharge spatio-temporal evolution under different flow regimes. This allows systematic comparison between laminar and turbulent flow operating conditions. The analysis focuses on plasma bullet propagation speed, discharge morphology, and electron number density distributions. Model predictions are assessed through qualitative comparison with optical emission data reported in the literature. The simulations capture experimentally observed trends in plasma bullet velocity and plume structure, indicating that large-scale flow structures play a measurable role in discharge propagation and species transport. These findings highlight the importance of macro-scale flow effects in modelling non-equilibrium plasma micro-jets.