  We develop an efficient approach for computing two-particle response
functions and interaction vertices for multiorbital strongly correlated systems
based on fluctuation around rotationally-invariant slave-boson saddle-point.
The method is applied to the degenerate three-orbital Hubbard-Kanamori model
for investigating the origin of the s-wave orbital antisymmetric spin-triplet
superconductivity in the Hund's metal regime, previously found in the dynamical
mean-field theory studies. By computing the pairing interaction considering the
particle-particle and the particle-hole scattering channels, we identify the
mechanism leading to the pairing instability around Hund's metal crossover
arises from the particle-particle channel, containing the local electron pair
fluctuation between different particle-number sectors of the atomic Hilbert
space. On the other hand, the particle-hole spin fluctuations induce the s-wave
pairing instability before entering the Hund's regime. Our approach paves the
way for investigating the pairing mechanism in realistic correlated materials.
