I decided this problem. The matter of it was SITE_ID in settings.py.
The facto of the matter that Flatpages from box has default site
example.com as default. If you create new your site before deleting
example.com you get SITE_ID: 2 and etc for your site. After that you
can delete
example.com but your site will be still with ID:2 and more.
However in settings.py you get as default SITE_ID:1. You have to be
carefully with SITE_ID if you are going to work with Flatpages.
Regards, George.