For those having trouble starting the game, here are two solutions:

a) make sure to keep your Flash-Plugin up-to-date and re-install if in doubt, e.g. from here:
https://get.adobe.com/de/flashplayer/?no_redirect

For Foirefox and other browsers use:
https://get.adobe.com/de/flashplayer/otherversions/

By experience the Firefox NPAPI Flash version works best. Choose your Operation System, then choose Firefox NPAPI.

b) Set up your game: choose between two versions of the Flash-Plugin if one is not working for you, by selecting Options/Plugin Settings from the main menu.

After installation, set up the Anno Online app as can be seen on this screenshot: