We perform a combined experimental-theoretical study of the Fe-oxychalcogenides (FeO\(\emph{Ch}\)) series La\(_{2}\)O\(_{2}\)Fe\(_{2}\)O\emph{M}\(_{2}\) (\emph{M}=S, Se), which is the latest among the Fe-based materials with the potential \ to show unconventional high-T\(_{c}\) superconductivity (HTSC). A combination of incoherent Hubbard features in X-ray absorption (XAS) and resonant inelastic X-ray scattering (RIXS) spectra, as well as resitivity data, reveal that the parent FeO\(\emph{Ch}\) are correlation-driven insulators. To uncover microscopics underlying these findings, we perform local density approximation-plus-dynamical mean field theory (LDA+DMFT) calculations that unravel a Mott-Kondo insulating state. Based upon good agreement between theory and a range of data, we propose that FeO\(\emph{Ch}\) may constitute a new, ideal testing ground to explore HTSC arising from a strange metal proximate to a novel selective-Mott quantum criticality.