FeRh shows an antiferromagnetic to ferromagnetic phase transition above room temperature, which permits its use as an antiferromagnetic memory element. However, its antiferromagnetic order is sensitive to small variations in crystallinity and composition, challenging its integration into flexible devices. Here, we show that flexible FeRh films of high crystalline quality can be synthesized by using mica as a substrate, followed by a mechanical exfoliation of the mica. The magnetic and transport data indicate that the FeRh films display a sharp antiferromagnetic to ferromagnetic phase transition. Magnetotransport data allow for the observation of two distinguishable resistance states, which are written after a field-cooling procedure. It is shown that the memory states are robust under the application of magnetic fields of up to 10 kOe.