Dear Mahdi,
for the reaction cross section there is no need for a thin target nor scoring yields and not even running more than one history. One shall just look at the material table in the standard output file and find the desired inelastic scattering length of the primary particle at beam energy. This allows you to calculate the reaction cross section at that energy, via the material density, atomic weight value (g/mol) and Avogadro number.
As for specific channels the reaction cross section is partitioned, then earlier discussions on this forum explained indeed a way to extract it through thin target geometry and yield scoring, recalling however that FLUKA was not conceived as a tool to extract partial cross sections, rather for the calculation of macroscopic yields.