It has been shown that the mode-aware dataflow (MADF) is an advantageous analysis model for adaptive streaming applications. However, no attention has been paid on how to implement and execute an application, modeled and analyzed with the MADF model, on a Multi-Processor System-on-Chip, such that the properties of the analysis model are preserved. Therefore, in this paper, we consider this matter and propose a generic parallel implementation and execution approach for adaptive streaming applications modeled with MADF. Our approach can be easily realized on top of existing operating systems while supporting the utilization of a wider range of schedules. In particular, we demonstrate our approach on LITMUS RT as one of the existing real-time extensions of the Linux kernel. Finally, to show the practical applicability of our approach and its conformity to the analysis model, we present a case study using a real-life adaptive streaming application.