Direct from the clementine site..
You can download the latest version of Clementine on Ubuntu from the official PPA.
Run these commands in the terminal:
sudo add-apt-repository ppa:me-davidsansome/clementine
sudo apt-get update
sudo apt-get install clementine
You will need to do this if you want the latest (or non-open) features.
Once you have updated if your still missing the plugin download button you can install manually. Instructions are here. You can download the plugin from this directory. Just put the blob and the plugin in ~/.config/Clementine/spotifyblob