This paper proposes an approach using spectral flatness measure to detect the glottal closure instant (GCI) and the glottal open region (GOR) within each glottal cycle in voiced speech. The spectral flatness measure is derived from the instantaneous spectra obtained in the analysis of speech using single frequency filtering (SFF) and zero time windowing (ZTW) methods. The Hilbert envelope of the numerator of group delay (HNGD) spectrum at each instant of time is obtained using the ZTW method. The HNGD spectrum highlights the important (like resonances) spectral characteristics of the vocal tract system at each instant of time. The dynamic characteristics of the vocal tract system can be tracked by the spectral flatness feature of the HNGD spectrum, thus bringing out the characteristics of the vocal tract system when the subglottal region is coupled with the supraglottal region during the open phase of the glottal cycle. The SFF spectra at each instant change significantly at the location of the GCI. The GCIs can be detected using the changes in the spectral flatness information derived from the SFF spectra. The proposed methods of detection of GCI and GOR is compared with several existing methods.