The paper proposes a Random Network Coding based solution for data dissemination applications involving multiple unicast or multicast transmissions between a source and several destinations. The solution proposed is based on a mathematical framework derived from the theory of Random Network Coding employed in multicast transmissions. This framework specifies the conditions allowing to each destination to decode only the flows of interest, when the total rate of the source flows is larger than the capacity of the network. A testbed, shortly described in the paper, was implemented for proof of concept and the performances of the coded transmissions were compared to that of uncoded transmissions. The results show the improvement brought by our solution in what concerns the packet loss rate obtained for different ratios between the source flows rates and the transfer rates of the test topology's bottleneck links.