You will need to install a user script manager extension to install this script.
It's awful but it works, I based it on this https://greasyfork.org/en/scripts/386709-soundcloud-download-button-generator
Fetches a new client id from the youtube-dl project every three days, so this script should work fine for a long time unless some dramatic change happens in either youtube-dl or soundcloud. Generates a download button and a direct link to the track file in both the stream view, and the song page. Doesn't work for playlists in the stream view yet.
Fixed in 1.4: direct download button always works