A lattice Kinetic Monte Carlo (KMC) approach is considered to study the statistical properties of the diffusion of Pt atom clusters on a Pt(111) surface. The interatomic potential experienced by the diffusing atoms is calculated by the embedded atom method and the hopping barrier for the allowed atomic movements are calculated using the Nudged Elastic Band method. The diffusion coefficient is computed for various cluster sizes and system temperatures. The obtained results are in agreement with the ones obtained in previous experimental and theoretical works. A simple scaling argument is proposed for the size dependence of the diffusion coefficient's prefactor. A detailed statistical analysis of the event by event KMC dynamics reveals two important and co-existing mechanisms for the diffusion of the cluster's center of mass. At low temperatures (below T=400K) the dominating mechanism responsible for the displacement of the cluster's center of mass is the periphery (or edge) diffusion of the atoms. At high temperatures (above T=800K) the dissociation and recombination of the clusters becomes more and more important.