Rotating detonation engines offer the promise of pressure gain combustion in aeronautical combustors where (normally) stagnation pressure decreases. For practical reasons, current experimental rotating detonation engine designs include separate streams of fuel and air injected into a detonation channel. Experimentation with a fully premixed rotating detonation engine has repeatedly failed due to flame flashback into the premixed plenum. That fundamental problem is the subject of this paper: understanding the relevant principles and parameters that contribute to flashback and investigating a scheme for arresting the flashback phenomenon. This investigation quantifies the flashback susceptibility for a proposed rotating detonation engine feed slot with parameterization of channel height, channel length, equivalence ratio, fuel type, and feed pressure. The design principles of quenching distance and critical boundary-layer velocity gradients are shown to describe the safe operation region to deliver a safe premixture of fuel and air to a rotating detonation engine when adjusted for experimental conditions and applied in unison. This research leads to a design that is capable of avoiding flashback while enabling detonation to occur in a rotating detonation engine.