Context. Understanding how the large-scale kinematics of the Milky Way (MW) shape the formation and evolution of the interstellar medium remains challenging from an observational perspective, and numerical models that can reproduce the observed structure and kinematics of the MW are much needed to be able to infer how the MW might work as a star formation engine. Aims. Our aim with this work is to use a numerical framework that is a close match to the observed large-scale distribution of stars and gas in the MW to isolate and understand the impact of galaxy-driven flows on the formation, agglomeration, and longevity of spiral patterns prior to the inclusion of chemistry, star formation, and feedback. Methods. We used an isothermal simulation of a MW-like galaxy found to closely match the longitude-velocity observational features of the MW by previous work that includes the coupled evolution of gas, stars, and dark matter under purely gravitational and hydrodynamical processes. We characterised the morphology and kinematics of the stars and gas in the disc, quantified velocity residuals and their association with spiral features, and analysed the time evolution of individual spiral-ridge segments. Results. Our results demonstrate that our model reproduces many of the observed structural and kinematic signatures of the MW, from the inner Galaxy to the solar neighbourhood, supporting its suitability as an analogue of the MW. The stellar spiral pattern in our model is relatively weak and shows a lower multiplicity relative to the sharper gaseous arms, offering an explanation for discrepancies in observational determinations of the number and location of MW spiral arms. Both the gas and stellar spiral arms are highly segmented, without a single coherent spiral pattern that would be expected from a grand-design type of galaxy. We find strong radial motions linked to the non-circular motions driven by the presence of a bar and that extend well into the disc. The gas radial and tangential velocity residuals can be as strong as 30─50 km s−1, with alternating patterns of converging and diverging flows (promoting the growth and dissolution of spiral arm segments), and they evolve over short timescales of ~10─20 Myr. This transient, dynamically driven nature of spiral structures could explain the observed low contrast in cloud properties and star formation occurring inside versus outside spiral arms in the MW.