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 Hα 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 * ∝ M 0.53 ± 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 g , Hα star formation rate surface density Σ SFR ) and its parameterised restframe UV / optical morphology (e.g. Sérsic index, bulge to total ratio, Clumpiness, Asymmetry and Concentration). We establish that the position in the j * -M * plane is 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.