  We present an analysis of the gas dynamics of star-forming galaxies at z~1.5
using data from the KMOS Galaxy Evolution Survey (KGES). We quantify the
morphology of the galaxies using $HST$ CANDELS imaging parametrically and
non-parametrically. We combine the H$\alpha$ dynamics from KMOS with the
high-resolution imaging to derive the relation between stellar mass (M$_{*}$)
and stellar specific angular momentum (j$_{*}$). We show that high-redshift
star-forming galaxies at z~1.5 follow a power-law trend in specific stellar
angular momentum with stellar mass similar to that of local late-type galaxies
of the form j$_*$$\propto$M$_*^{0.53 \pm 0.10}$. The highest specific angular
momentum galaxies are mostly disc-like, although generally, both peculiar
morphologies and disc-like systems are found across the sequence of specific
angular momentum at a fixed stellar mass. We explore the scatter within the
j$_{*}$-M$_{*}$ plane and its correlation with both the integrated dynamical
properties of a galaxy (e.g. velocity dispersion, Toomre Q$_{\rm g}$, H$\alpha$
star formation rate surface density $\Sigma_{\rm SFR}$) and its parameterised
rest-frame UV/optical morphology (e.g. S\'ersic index, bulge to total ratio,
Clumpiness, Asymmetry and Concentration). We establish that the position in the
j$_{*}$-M$_{*}$ plane is strongly correlated with the star-formation surface
density and the Clumpiness of the stellar light distribution. Galaxies with
peculiar rest-frame UV/optical morphologies have comparable specific angular
momentum to disc-dominated galaxies of the same stellar mass, but are clumpier
and have higher star-formation rate surface densities. We propose that the
peculiar morphologies in high--redshift systems are driven by higher star
formation rate surface densities and higher gas fractions leading to a more
clumpy inter-stellar medium.
