The ZFIRE survey has spectroscopically confirmed two proto-clusters using the MOSFIRE instrument on Keck I: One at z = 2.095 in COSMOS and another at z = 1.62 in UKIRT Infrared Deep Sky Survey (UDS). Here, we use an updated ZFIRE data set to derive the properties of ionized gas regions of proto-cluster galaxies by extracting fluxes from emission lines Hβ 4861 Å, [O iii] 5007 Å, Hα 6563 Å, [N ii] 6585 Å, and [S ii] 6716,6731 Å. We measure gas-phase metallicity of members in both proto-clusters using two indicators, including a strong-line indicator relatively independent of the ionization parameter and electron density. Proto-cluster and field galaxies in both UDS and COSMOS lie on the same Mass-Metallicity Relation with both metallicity indicators. We compare our results to recent IllustrisTNG results, which report no significant gas-phase metallicity offset between proto-cluster and field galaxies until z = 1.5. This is in agreement with our observed metallicities, where no offset is measured between proto-cluster and field populations. We measure tentative evidence from stacked spectra that indicate UDS high-mass proto-cluster and field galaxies have differing [O iii]/Hβ ratios; however, these results are dependent on the sample size of the high-mass stacks