We perform a kinematic and morphological analysis of 44 star-forming galaxies at z \sim 2 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 \pm 0.07 ) \log ( M / M _ { \odot } -10 ) + ( 2.04 \pm 0.03 ) with no significant offset between morphological populations and similar levels of scatter ( \sim 0.16 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 \pm 0.12 , 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 .