In this work, we develop a kinetic Monte Carlo (KMC) scheme to describe 1-D migration in a field of traps. The model is parameterized solely on static calculations but is capable to predict the evolution of the system at finite temperature. The model is parameterized to describe the migration of self-interstitial clusters in the W-Re system that is of particular interest for fusion applications. The developed KMC model is benchmarked against molecular dynamics simulations and is found suitable to replace the latter at a fraction of the computational cost. We found that the presence of even traces of Re (starting from 0.1%) has a significant impact on the mobility of small 1-D migrating self-interstitial clusters. In addition to the computational scheme, the obtained results elucidate the impact of Re on void swelling and the suppression of void lattice formation under neutron irradiation of tungsten.