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I'm running MD simulations using VASP to predict the lattice thermal conductivity of Cu and I need to know the potential and kinetic energies of individual atoms in my system. I know the total potential and kinetic energies can be directly output by VASP, but I have no idea about how to get the energies for individual atoms. I'll be appreciated if you could give me some help on this subject.

In abinitio MD the total energy is not defined as a sum of atomic components.
The subdivision of the potential energy to atomic components is not possible.
The kinetic energy of a single atom is E_{kin}=1/2m_i v_i^2.
In NVT ensemble the average kinetic energy of the atom is 3/2 k_b T.

Thanks for the reply.
Plus: Does VASP has the functionality for calculating thermal conductivity?

Yes, any code that determines Hellmann-Feynmann forces can be used.
Cf. e.g. PRB 104(2010)208501.