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Stellar feedback-driven outflows regulate the stellar formation and chemical enrichment of galaxies, yet the underlying dependence of mass outflow rate on galaxy properties remains largely unknown. We develop a simple yet comprehensive non-equilibrium chemical evolution model~(NE-CEM) to constrain the mass-loading factor $\eta$ of outflows using the metallicity-stellar mass-SFR relation observed by SDSS at $z{=}0$. Our NE-CEM predicts the chemical enrichment by explicitly tracking both the histories of star formation and mass-loading. After exploring the EAGLE simulation, we discover a compact yet flexible model that accurately describes the average star formation histories of galaxies. Applying a novel method of chemically measuring $\eta$ to EAGLE, we find $\eta$ can be parametrised by its dependence on stellar mass and specific SFR as $\log\eta\propto M_*^{\alpha}s{\mathrm{SFR}}^{\beta}$, with $\alpha{=}{-}0.12$ and $\beta{=}0.32$ in EAGLE. Our chemically-inferred $\eta$ agrees remarkably well with the kinematic measurements by Mitchell et al. After extensive tests with EAGLE, we apply an NE-CEM Bayesian analysis to the SDSS data, yielding a tight constraint of $\log(\eta/0.631)=0.731{\pm}0.002\times(M_*/10^{9.5}M_{\odot})^{-0.222\pm0.004} (s{\mathrm{SFR}}/10^{-9.5}yr^{-1})^{0.078\pm0.003}$, in good agreement with the down-the-barrel measurements. Our best-fitting NE-CEM not only accurately describes the metallicity-stellar mass-SFR relation at $z{=}0$, but also successfully reproduce the so-called "fundamental metallicity relation'' at higher redshifts. Our results reveal that different galaxies form stars and enrich their gas in a non-equilibrium but strikingly coherent fashion across cosmic time., Comment: 22 pages, 17 figures, with key results in Fig. 13, 15, & 16. Comments welcome! Fixed a typo in the \eta parameterization and relevant annotations in the figures. Conclusion unchanged