  We show that a holographic description of four-dimensional asymptotically
locally flat spacetimes is reached smoothly from the zero-cosmological-constant
limit of anti-de Sitter holography. To this end, we use the derivative
expansion of fluid/gravity correspondence. From the boundary perspective, the
vanishing of the bulk cosmological constant appears as the zero velocity of
light limit. This sets how Carrollian geometry emerges in flat holography. The
new boundary data are a two-dimensional spatial surface, identified with the
null infinity of the bulk Ricci-flat spacetime, accompanied with a Carrollian
time and equipped with a Carrollian structure, plus the dynamical observables
of a conformal Carrollian fluid. These are the energy, the viscous stress
tensors and the heat currents, whereas the Carrollian geometry is gathered by a
two-dimensional spatial metric, a frame connection and a scale factor. The
reconstruction of Ricci-flat spacetimes from Carrollian boundary data is
conducted with a flat derivative expansion, resummed in a closed form in
Eddington-Finkelstein gauge under further integrability conditions inherited
from the ancestor anti-de Sitter set-up. These conditions are hinged on a
duality relationship among fluid friction tensors and Cotton-like geometric
data. We illustrate these results in the case of conformal Carrollian perfect
fluids and Robinson-Trautman viscous hydrodynamics. The former are dual to the
asymptotically flat Kerr-Taub-NUT family, while the latter leads to the
homonymous class of algebraically special Ricci-flat spacetimes.
