The Study of H$\alpha$ from Dwarf Emissions (SH$\alpha$DE) is a high spectral resolution (R=13500) H$\alpha$ integral field survey of 69 dwarf galaxies with stellar masses $10^6<M_\star<10^9 \,\rm{M_\odot}$. The survey used FLAMES on the ESO Very Large Telescope. SH$\alpha$DE is designed to study the kinematics and stellar populations of dwarf galaxies using consistent methods applied to massive galaxies and at matching level of detail, connecting these mass ranges in an unbiased way. In this paper we set out the science goals of SH$\alpha$DE, describe the sample properties, outline the data reduction and analysis processes. We investigate the $\log{M_{\star}}-\log{S_{0.5}}$ mass-kinematics scaling relation, which have previously shown potential for combining galaxies of all morphologies in a single scaling relation. We extend the scaling relation from massive galaxies to dwarf galaxies, demonstrating this relation is linear down to a stellar mass of $M_{\star}\sim10^{8.6}\,\rm{M_\odot}$. Below this limit, the kinematics of galaxies inside one effective radius appear to be dominated by the internal velocity dispersion limit of the H$\alpha$-emitting gas, giving a bend in the $\log{M_{\star}}-\log{S_{0.5}}$ relation. Replacing stellar mass with total baryonic mass using gas mass estimate reduces the severity but does not remove the linearity limit of the scaling relation. An extrapolation to estimate the galaxies' dark matter halo masses, yields a $\log{M_{h}}-\log{S_{0.5}}$ scaling relation that is free of any bend, has reduced curvature over the whole mass range, and brings galaxies of all masses and morphologies onto the virial relation.