  The flat/CFT dictionary between the bulk gravitational theory and boundary
conformal field theory is systematically developed in this paper.
Asymptotically flat spacetime is built up by asymptotically AdS hyperboloid
slices in terms of Fefferman Graham coordinates together with soft modes
propagating between different slices near the null boundary. Then we construct
the flat holography dictionary based on studying Einstein equation at zero and
first order and it turns out that these correspond to the description of hard
and soft sector for the field theory from the boundary point of view. The
explicit expression for energy-stress tensor is also determined by performing
holographic renormalisation on the Einstein Hilbert action. By studying the
anomalies of the energy-stress tensor, we obtain the leading and subleading
contribution to the central charge. Einstein equations in the bulk are related
to the Ward identities of the boundary theory and we find that the boundary CFT
energy-stress tensor is not conserved due to the existence of radiative soft
modes which will generate the energy flow through the null boundary.
