After lots of googling, testing, reading and so on, I've finally found out the Drush command to flush the cache of a single Drupal (8) site in a multi-site setup.
drush -l 8888.notes cache-rebuild
If your site is located at /sites/8888.notes you need the command above. The "-l" parameter is necessary. I could not find out what "-l" means, but this parameter seemed necessary.