You have to find a way to get the audio streaming from Spotify to the MP3 format or something that's supported and then you can load it in Amazing Slow Downer. Unfortunately, ripping the audio stream from Spotify service is against their ToS. There were some apps at one point that offered the possibility to save to MP3 what you were listening, but they're long gone.
You can record the audio stream with an app and then load it in Spotify. For that to happen, you need to enable Stereo Mix in the Recording window.