In this work, we explore the diversity of ionised gas kinematics (rotational velocity $v_{phi}$ and velocity dispersion $sigma_{mathrm{g}}$) and gas-phase metallicity gradients at $0.1 leq z leq 2.5$ using a compiled data set of 74 galaxies resolved with ground-based integral field spectroscopy. We find that galaxies with the highest and the lowest $sigma_{mathrm{g}}$ have preferentially flat metallicity gradients, whereas those with intermediate values of $sigma_{mathrm{g}}$ show a large scatter in the metallicity gradients. Additionally, steep negative gradients appear almost only in rotation-dominated galaxies ($v_{phi}/sigma_{mathrm{g}} > 1$), whereas most dispersion-dominated galaxies show flat gradients. We use our recently developed analytic model of metallicity gradients to provide a physical explanation for the shape and scatter of these observed trends. In the case of high $sigma_{mathrm{g}}$, the inward radial advection of gas dominates over metal production and causes efficient metal mixing, thus giving rise to flat gradients. For low $sigma_{mathrm{g}}$, it is the cosmic accretion of metal-poor gas diluting the metallicity that gives rise to flat gradients. Finally, the reason for intermediate $sigma_{mathrm{g}}$ showing the steepest negative gradients is that both inward radial advection and cosmic accretion are weak as compared to metal production, which leads to the creation of steeper gradients. The larger scatter at intermediate $sigma_{mathrm{g}}$ may be due in part to preferential ejection of metals in galactic winds, which can decrease the strength of the production term. Our analysis shows how gas kinematics play a critical role in setting metallicity gradients in high-redshift galaxies.
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