If you have resorted to Google after having uselessly pored over AD’s reference manuals, hoping to find at least a proper hint about how to approach this, if not a bit of code, it’s OK, you can stop now. It’s right here. Your quest is complete.
In the hope that no poor soul will have to bang his head against the desk trying to piece together the countless pieces of this puzzle, I did a quick write-up to show you how to do SPI communication with DMA on ADSP-21489. This should probably work (with obvious adaptation) on any DSP in the same family, and it should be easy to adapt if your DSP is the SPI slave, not the master, as below.