I suppose that you don't want to have a public group to not allow anybody to read and see everything that people post, what I may understand in some situation.
When you create a private group, nobody will see such group publicly excepted if you advertise it on your profile or business page, or if you invite people by email, or otherwise, to become member of your group.
So, my suggestion would be to create 2 groups exactly the same. One which is public and one which is private.
When people join the public group, you may look at their profile if they seem interesting for your group and you invite them to join the private one.
In addition, you may even write on your public group, which will be seen by everybody, even by people who are not users of Flokii, the existence of the private group.
Hope it's helping you.