We perform a kinematic and morphological analysis of 44 star-forming galaxies at $zsim2$ in the COSMOS legacy field using near-infrared spectroscopy from Keck/MOSFIRE and F160W imaging from CANDELS/3D-HST as part of the ZFIRE survey. Our sample consists of cluster and field galaxies from $2.0 < z < 2.5$ with K band multi-object slit spectroscopic measurements of their H$alpha$ emission lines. H$alpha$ rotational velocities and gas velocity dispersions are measured using the Heidelberg Emission Line Algorithm (HELA), which compares directly to simulated 3D data-cubes. Using a suite of simulated emission lines, we determine that HELA reliably recovers input S$_{0.5}$ and angular momentum at small offsets, but $V_{2.2}/sigma_g$ values are offset and highly scattered. We examine the role of regular and irregular morphology in the stellar mass kinematic scaling relations, deriving the kinematic measurement S$_{0.5}$, and finding $log(S_{0.5}) = (0.38pm0.07)log(M/M_{odot}-10) + (2.04pm0.03)$ with no significant offset between morphological populations and similar levels of scatter ($sim0.16$ dex). Additionally, we identify a correlation between M$_{star}$ and $V_{2.2}/sigma_g$ for the total sample, showing an increasing level of rotation dominance with increasing M$_{star}$, and a high level of scatter for both regular and irregular galaxies. We estimate the specific angular momenta ($j_{disk}$) of these galaxies and find a slope of $0.36pm0.12$, shallower than predicted without mass-dependent disk growth, but this result is possibly due to measurement uncertainty at M$_{star}$ $<$ 9.5. However, through a K-S test we find irregular galaxies to have marginally higher $j_{disk}$ values than regular galaxies, and high scatter at low masses in both populations.
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