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How can I calculate the spin exchange interaction parameters J for any magnetic material in VASP?

Calculate the total energy of your system in various types of spin ordering (one Ferro and some possible Antiferro ordering), and then, fit these energies to Heisenberg Hamiltonian (${\hat{\mit H}} = -\sum\nolimits_{i<j} J_{ij}S_{i}S_{j}$) to get $ J_{ij}$ of pairs of interactions.
To define different spin configurations you should use MAGMOM-tag in your INCAR file. You might (depend on you system) also need to make supercell out of you initial structure to define Antiferromagnetic ordering.
I hope this can help.

Cheers,
Salman