We consider the possibility that the lightest supersymmetric particle in flipped SUSY SU(5) × U(1) models is cosmologically stable and corresponds to a neutralino. Previous studies of dark matter in flipped SUSY SU(5) models have suggested that the decay of the oscillations of the SU(5) breaking scalar field would result in too many neutralinos, if they are stable. We show that it is possible for an acceptable density of neutralinos to occur in the case where the neutralino corresponds to a light photino, if the temperature at the end of the oscillation dominated period is <O(10)MeV. This leads to the possibility of directly detectable dark matter in flipped SU(5) models. Direct detection of dark matter in forthcoming experiments will therefore not eliminate this class of models.