Providing multi-connectivity services is an important goal for next generation wireless networks, where multiple access networks are available and need to be integrated into a coherent solution that efficiently supports both reliable and non reliable traffic. Based on virtual network interfaces and per path congestion controlled tunnels, the MP-DCCP based multiaccess aggregation framework presents a novel solution that flexibly supports different path schedulers and congestion control algorithms as well as reordering modules. The framework has been implemented within the Linux kernel space and has been tested over different prototypes. Experimental results have shown that the overall performance strongly depends upon the congestion control algorithm used on the individual DCCP tunnels, denoted as CCID. In this paper, we present an implementation of the BBR (Bottleneck Bandwidth Round Trip propagation time) congestion control algorithm for DCCP in the Linux kernel. We show how BBR is integrated into the MP-DCCP multi-access framework and evaluate its performance over both single and multi-path environments. Our evaluation results show that BBR improves the performance compared to CCID2 (TCPlike Congestion Control) for multi-path scenarios due to the faster response to changes in the available bandwidth, which reduces latency and increases performance, especially for unreliable traffic. The MP-DCCP framework code, including the new CCID5 is available as OpenSource1.