  We show that by studying the flat spacetime limit of the Mellin amplitude
associated with the four-point correlation function of scalar operators in the
stress tensor multiplet of ABJM theory, one can produce the momentum expansion
of the M-theory four-graviton S-matrix elements. Using CFT data previously
obtained from the supersymmetric localization method, we carry out this
procedure explicitly to the second nontrivial order in the momentum expansion,
and recover precisely the known $R^4$ contribution to the scattering amplitude
of super-gravitons in M-theory in eleven dimensions.
