Since the Arduino UNO has very limited RAM we need to put the data somewhere. The Catalex MicroSD card reader provides us with the storage we need, is relatively cheap and sold at Kjell o Co (The MicroSD cards on the other hand might be a tad expensive). The second thing we need is an amplifying circuit – a basic one with only a single transistor should do.
And it works! Used a P2N2222 transistor as an amplifier. Then something corrupted the SD Card. Might have been one of two things: Either it needs more power – plugged in the external power cable, or it could have been that I tried to write to the SD while sound still was playing (since it streams from card). Last one is the likely issue.