The shields, that I want to plug in to the Particle shield shield, all require Arduino Uno compatibility.
I’ve seen “Arduino compatible” for the the Particle shield shield datasheet but search doesn’t show “Arduino Uno” anywhere.
Arduino Uno is the generic Arduino board, any Arduino Uno shield is also compatible with other Arduino boards and the Particle shield shield.
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But compatibility is a relative term here.
Not every Arduino shield that fits into the Shield shield will be fully functional in it.
You’d need to check the required pin functions on the respective pins.
If you could state what shields you intend to use, we might be able to give you a “rough” answer if that particular shield should work or not - but still no guarantees unless we have the shield to test ourselves 
I would so appreciate that!
Adafruit’s MUSIC MAKER is the shield
It would be fantastic if it would run on your shield shield with a Photon.
Then, audio can be downloaded though Photon’s WiFi.
That looks like a breakout and not a shield. It could be possible to use it with a Photon.
Adafruit’s Music Maker and Particle’s Photon an a shield shield.
Music Maker is a shield ‘relative’ to an Arduino UNO.
I’m investigating a Particle forum article that hints that Photon may be compatible with Music Maker on a shield. Here
I want to get Music Maker’s VS1053 Github library running on the Photon.
Sorry. The adafruit tutorial was for the breakout.
Here is the library that @peekay123 wrote. https://github.com/pkourany/Adafruit_VS1053_Library