We present an analysis of spatially resolved gas-phase metallicity relations in five dwarf galaxies ($M_{halo} \approx 10^{11} M_\odot$, $M_\star \approx 10^{8.8}-10^{9.6} M_\odot$) from the FIRE-2 (Feedback in Realistic Environments) cosmological zoom-in simulation suite, which include an explicit model for sub-grid turbulent mixing of metals in gas, near $z\approx 0$, over a period of 1.4 Gyrs, and compare our findings with observations. While these dwarf galaxies represent a diverse sample, we find that all simulated galaxies match the observed mass-metallicity (MZR) and mass-metallicity gradient (MZGR) relations. We note that in all five galaxies, the metallicities are effectively identical between phases of the interstellar medium (ISM), with 95$\%$ being within $\pm$0.1 dex between various ISM phases, including the cold and dense gas ($T < 500$ K and $n_{\rm H} > 1$ cm$^{-3}$), ionized gas (near the H$\alpha$ $T \approx 10^4$ K ridge-line), and nebular regions (ionized gas where the 10 Myr-averaged star formation rate is non-zero). We find that most of the scatter in relative metallicity between cold and dense gas and ionized gas/nebular regions can be attributed to either local starburst events or metal-poor inflows. We also note the presence of a major merger in one of our galaxies, m11e, with a substantial impact on the metallicity distribution in the spatially resolved map, showing two strong metallicity peaks and triggering a starburst in the main galaxy.