I have a view with lists of 10 nodes with a node display type (not rows). Every node has a flag. How to make possible to flag ONLY one node of these 10 nodes, for example if you have flagged one node - you cannot flag another one untill you unflag flagged one. Just like a best answer functionality on this site. Thanks :)
You're looking for the Flag trim action, which you can implement with Rules.
If you make a rule that is activated on the event "Node is flagged" with "Trim the flag" for the relevant user to "1", then the other flags will be cancelled and only the most recent flag will remain.
Is Flag Limit module what you are looking for?
This module allows any flag (for example: bookmarks) to have a limited number of items.
There is a new feature in the 7.x-1.x branch that optionally lets you limit the number of flaggings each item can have. Once the limit is reached, nobody else can flag the item.