Kinship prediction in forensics is limited to first degree relatives due to the small number of short tandem repeat loci characterized. The Genetic Chain Rule for Probabilistic Kinship Estimation can leverage large panels of single nucleotide polymorphisms (SNPs) or sets of sequence linked SNPs, called haploblocks, to estimate more distant relationships between individuals. This method uses allele frequencies and Markov Chain Monte Carlo methods to determine kinship probabilities. Allele frequencies are a crucial input to this method. Since these frequencies are estimated from finite populations and many alleles are rare, a Bayesian extension to the algorithm has been developed to determine credible intervals for kinship estimates as a function of the certainty in allele frequency estimates. Generation of sufficiently large samples to accurately estimate credible intervals can take significant computational resources. In this paper, we leverage hundreds of compute cores to generate large numbers of Dirichlet random samples for Bayesian kinship prediction. We show that it is possible to generate 2,097,152 random samples on 32,768 cores at a rate of 29.68 samples per second. The ability to generate extremely large number of samples enables the computation of more statistically significant results from a Bayesian approach to kinship analysis.