No. A region of a piece of material is magnetized in a certain direction when its (ionized) atoms are mostly oriented in that direction, the presence of a const

No. A region of a piece of material is magnetized in a certain direction when its (ionized) atoms are mostly oriented in that direction, the presence of a constant magnetic field is (roughly speaking) only a consequence of that. So flash memory is about the electrons, while magnetic memory is about the ions.