Flexible and scalable decentralized learning solutions are fundamentally important in the application of multi-agent systems. While several recent approaches introduce (ensembles of) kernel machines in the distributed setting, Bayesian solutions are much more limited. We introduce a fully decentralized, asymptotically exact solution to computing the random feature approximation of Gaussian processes. We further address the choice of hyperparameters by introducing an ensembling scheme for Bayesian multiple kernel learning based on online Bayesian model averaging. The resulting algorithm is tested against Bayesian and frequentist methods on simulated and real-world datasets.