A time scale analysis of the homogeneous flame inhibition problem is carried out to identify the main parameters controlling the gas phase chemical interaction of the alkali metal inhibitors with the flame chemistry. First, kinetic sub-models for the interaction of alkali metals with the flame are analyzed to show that a simplified 2-step inhibition cycle can capture the essential features of this interaction. Second, it is shown that this cycle is auto-catalytic, which explains the high efficiency of alkali metals in inhibiting flames even at low concentrations. Third, the time scales associated to this inhibition cycle are linked to the free flame termination time scale via a non-dimensional parameter characterizing the efficiency of an inhibitor at promoting radical scavenging. It is shown that this parameter accounts for the main trends observed in the literature and can also be used to provide estimates for the chemical flame suppression limit.