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We measure resolved (kiloparsec-scale) outflow properties in a sample of 10 starburst galaxies from the DUVET (Deep near-UV observations of Entrained gas in Turbulent galaxies) sample, using Keck/KCWI observations of H$\beta$ and [OIII]~$\lambda$5007. We measure $\sim460$ lines-of-sight that contain outflows, and use these to study scaling relationships of outflow velocity ($v_{\rm out}$), mass-loading factor ($\eta$; mass outflow rate per SFR) and mass flux ($\dot{\Sigma}_{\rm out}$; mass outflow rate per area) with co-located SFR surface density ($\Sigma_{\rm SFR}$) and stellar mass surface density ($\Sigma_{\ast}$). We find strong, positive correlations of $\dot{\Sigma}_{\rm out} \propto \Sigma_{\rm SFR}^{1.2}$ and $\dot{\Sigma}_{\rm out} \propto \Sigma_{\ast}^{1.5}$. We also find shallow correlations between $v_{\rm out}$ and both $\Sigma_{\rm SFR}$ and $\Sigma_{\ast}$. Our resolved observations do not suggest a threshold in outflows with $\Sigma_{\rm SFR}$, but rather we find that the local specific SFR ($\Sigma_{\rm SFR}/\Sigma_\ast$) is a better predictor of where outflows are detected. We find that outflows are very common above $\Sigma_{\rm SFR}/\Sigma_\ast\gtrsim 0.1$~Gyr$^{-1}$ and rare below this value. We argue that our results are consistent with a picture in which outflows are driven by supernovae, and require more significant injected energy in higher mass surface density environments to overcome local gravity. The correlations we present here provide a statistically robust, direct comparison for simulations and higher redshift results from JWST.