I believe the Hamiltonian and exchange energy equations should be known from what was used to compute the exchange values from your DFT calculation. The DFT Hamiltonian might be defined differently depending on what program you have used (VASP, QE, WIEN2k, SIESTA, or other). By comparing that to VAMPIRE's Hamiltonian definition, the factor and/or unit differences between the two should be determinable.
The VAMPIRE Hamiltonian given under the FAQ question "There are numerous definitions of the exchange in the literature. How do I calculate the exchange constant for vampire?" that should be at [1], you might find helpful.
Kind Regards,
Gavin
VAMPIRE user