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We study an inequality between a scaling exponent $A$ in the Regge limit oftree-level flat space S-matrices with external massless scalars and anotherscaling exponent $A'$ in the Regge limit of the corresponding four-point scalarconformal correlators by using scaling exponents of Mellin amplitudes. Wederive $A'\ge A$, which leads to the Regge growth bound of tree-level flatspace S-matrices from the chaos bound in the flat space limit of the AdS/CFTcorrespondence, from polynomial boundedness of the Mellin amplitudes for localbulk descriptions. We also show $A'=A$ from the conformal block expansion inthe $t$-channel with finite intermediate spins when coefficients are not smallin the flat space limit.

Scaling exponents of Mellin amplitudes for deriving bounds on flat space S-matrices from bounds on chaos