In order to control and manage highly aggregated Internet traffic flows efficiently, we need to be able to categorize flows into distinct classes and to be knowledgeable about the different behavior of flows belonging to these classes. In this paper we consider the problem of classifying BGP level prefix flows into a small set of homogeneous classes. We argue that using the entire distributional properties of flows can have significant benefits in terms of quality in the derived classification. We propose a method based on modeling flow histograms using Dirichlet Mixture Processes for random distributions. We present an inference procedure based on the Simulated Annealing Expectation Maximization algorithm that estimates all the model parameters as well as flow membership probabilities - the probability that a flow belongs to any given class. One of our key contributions is a new method for Internet flow classification. We show that our method is powerful in that it is capable of examining macroscopic flows while simultaneously making fine distinctions between different traffic classes. We demonstrate that our scheme can address issues with flows being close to class boundaries and the inherent dynamic behaviour of Internet flows.