We investigate the relationship between star formation activity and outflow properties on kiloparsec scales in a sample of 28 star forming galaxies at $zsim$ 2-2.6, using adaptive optics assisted integral field observations from SINFONI on the VLT. The narrow and broad components of the H$alpha$ emission are used to simultaneously determine the local star formation rate surface density ($Sigma_{rm SFR}$), and the outflow velocity $v_{rm out}$ and mass outflow rate $dot{M}_{rm out}$, respectively. We find clear evidence for faster outflows with larger mass loading factors at higher $Sigma_{rm SFR}$. The outflow velocities scale as $v_{rm out}$ $propto$ $Sigma_{rm SFR}^{0.34 pm 0.10}$, which suggests that the outflows may be driven by a combination of mechanical energy released by supernova explosions and stellar winds, as well as radiation pressure acting on dust grains. The majority of the outflowing material does not have sufficient velocity to escape from the galaxy halos, but will likely be re-accreted and contribute to the chemical enrichment of the galaxies. In the highest $Sigma_{rm SFR}$ regions the outflow component contains an average of $sim$45% of the H$alpha$ flux, while in the lower $Sigma_{rm SFR}$ regions only $sim$10% of the H$alpha$ flux is associated with outflows. The mass loading factor, $eta$ = $dot{M}_{rm out}$/SFR, is positively correlated with $Sigma_{rm SFR}$ but is relatively low even at the highest $Sigma_{rm SFR}$: $eta lesssim$ 0.5 $times$ (380 cm$^{-3}$/n$_e$). This may be in tension with the $eta$ $gtrsim$ 1 required by cosmological simulations, unless a significant fraction of the outflowing mass is in other gas phases and has sufficient velocity to escape the galaxy halos.
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