Employing the I-concurrence (Ic) measure, entanglement dynamics of superposition of isospin fermionic coherent states (SFCS) in Heisenberg spin chains of Ising, XX, XXX and XXZ models in the presence of Dzyaloshinskii-Moriya (DM) interaction and magnetic field is studied. For the above-mentioned models, the entanglement dynamics of SFCSs is independent of magnetic field effect and the DM interaction effect introduces the quantum fluctuations in the entanglement dynamics of the system. It is shown that depending on the choice of the models in the absence of DM interaction, entanglement dynamics alter by applying and increasing the magnetic field to the first (second) part of the system. We showed that by increasing the spin of the fermionic coherent states (j) and, consequently, increasing their dimension d = 2j + 1, the entanglement dynamics of the SFCS states sharply increases and fluctuates at a higher level. Our results indicate no entanglement sudden death phenomenon under the examined conditions.