This paper addresses the problem of efficiently delivering a layered media stream from multiple senders to a single receiver, over channels that present correlated packet loss patterns. Using a digital fountain approach, the performance of a distributed streaming system is driven by the probability of receiving a given number of packets on aggregate over the multiple channels. In addition, such a system allows to avoid the need for communication between streaming servers. We devise an optimization problem whose solution provides the optimal number of packets that need to be transmitted per channel, in order to maximize the probability of correct decoding for a given media stream. Our findings indicate that it is in general important to consider both the Packet Loss Ratio (PLR) and Average Burst Length (ABL) in channel selection problems such as multipath routing or rate aggregation on multiple bursty channels. Finally we present a low-complexity algorithm which is able to quickly find a suboptimal yet effective solution to the combinatorial optimization problem.