  We perform a kinematic and morphological analysis of 44 star-forming galaxies
at $z\sim2$ 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 $\log(S_{0.5}) = (0.38\pm0.07)\log(M/M_{\odot}-10) +
(2.04\pm0.03)$ 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 $0.36\pm0.12$, 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.
