We consider Bayesian point and interval estimation for a risk ratio of two proportion parameters using two independent samples of binary data subject to misclassification. In order to obtain model identifiability, we apply a double sampling scheme. For the identifiable model, we propose a Bayesian method for statistical inference for a two proportion risk ratio. Specifically, we derive an easy-to-implement closed-form sampling algorithm to draw from the posterior distribution of interest. We demonstrate the efficiency of our algorithm for Bayesian inference via Monte Carlo simulation studies and using a real data example.