First problem is that both the BLE and MP3 shield use pins D8 and D9. This needs to be separated. See http://www.youtube.com/watch?v=behMgV3tUr4 as how to bend and reroute pins on a shield. And then correspondingly change the pin definition in the corresponding library.
After that there may be some other conflicts. Next thought about SPI conflicts, appears to be ok, as a quick (not extensive look) at their library shows the SPI is default for the AVR and should be compatible.
They don’t really provide schematics. so hard to tell about much else.
And their demo code is quite extensive. To much so to quickly assess. Where it appears a prinicpal function is to take control of all the AVR’s pins and remote them from the APP. This is would be bad. Where your use would be to have a remote APP control this libraries functions and not the pins themselves.
