In order to get the latest Docker Compose to work on my Raspbery Pi 3 running Raspbian (OSMC) I had to follow these steps:
sudo apt-get install build-essential libssl-dev libffi-dev python3-dev
sudo pip3 install cryptography
sudo pip3 install docker-compose
Then you can check the version:
docker-compose --version
Thanks to nitvit610 on Reddit.