We present updated metallicity relations for the spectral database of star-forming galaxies (SFGs) found in the KPNO International Spectroscopic Survey (KISS). New spectral observations of emission-line galaxies (ELGs) obtained from a variety of telescope facilities provide oxygen abundance information. A nearly four-fold increase in the number of KISS objects with robust metallicities relative to our previous analysis provides for an empirical abundance calibration to compute self-consistent metallicity estimates for all SFGs in the sample with adequate spectral data. In addition, a sophisticated spectral energy distribution (SED) fitting routine has provided robust calculations of stellar mass. With these new and/or improved galaxy characteristics, we have developed luminosity-metallicity ($L-Z$) relations, mass-metallicity ($M_{*}-Z$) relations, and the so-called Fundamental Metallicity Relation (FMR) for over 1,450 galaxies from the KISS sample. This KISS $M_{*}-Z$ relation is presented for the first time and demonstrates markedly lower scatter than the KISS $L-Z$ relation. We find that our relations agree reasonably well with previous publications, modulo modest offsets due to differences in the SEL metallicity calibrations used. We illustrate an important bias present in previous $L-Z$ and $M_{*}-Z$ studies involving direct-method ($T_{e}$) abundances that may result in systematically lower slopes in these relations. Our KISS FMR shows consistency with those found in the literature, albeit with a larger scatter. This is likely a consequence of the KISS sample being biased toward galaxies with high levels of activity.