We compare galaxy scaling relations as a function of environment at z~2 with our ZFIRE survey where we have measured H{alpha} fluxes for 90 star-forming galaxies selected from a mass-limited (log(M_*_/M_{sun}_)>9) sample based on ZFOURGE. The cluster galaxies (37) are part of a confirmed system at z=2.095 and the field galaxies (53) are at 1.9<z<2.4; all are in the COSMOS legacy field. There is no statistical difference between H{alpha}-emitting cluster and field populations when comparing their star formation rate (SFR), stellar mass (M_*_), galaxy size (r_eff_), SFR surface density ({Sigma}(H{alpha}_star_)), and stellar age distributions. The only difference is that at fixed stellar mass, the H{alpha}-emitting cluster galaxies are log(r_eff_)~0.1 larger than in the field. Approximately 19% of the H{alpha} emitters in the cluster and 26% in the field are IR-luminous (L_IR_>2x10^11^L_{sun}_). Because the luminous IR galaxies in our combined sample are ~5 times more massive than the low-IR galaxies, their radii are ~70% larger. To track stellar growth, we separate galaxies into those that lie above, on, or below the H{alpha} star-forming main sequence (SFMS) using {Delta}SFR(M*)=+/-0.2dex. Galaxies above the SFMS (starbursts) tend to have higher H{alpha} SFR surface densities and younger light-weighted stellar ages than galaxies below the SFMS. Our results indicate that starbursts (+SFMS) in the cluster and field at z~2 are growing their stellar cores. Lastly, we compare to the (SFR-M*) relation from Rhapsody-G cluster simulations and find that the predicted slope is nominally consistent with the observations. However, the predicted cluster SFRs tend to be too low by a factor of ~2, which seems to be a common problem for simulations across environment.