When setting off a person's age, one uses comma before and after:
John, 18, lives in France.
Is it proper to do the same when "John" is possessive? For example: John's, 18, labrador is white.
You should not do this when the noun takes a possessive form.
Instead, avoid the use of the possessive form and rewrite the sentence to show possession in another way, like this:
John, 18, has a white labrador.
The problem with trying to mix together a statement of John's age and the statement that he has a white labrador is that it becomes difficult for the reader to tell if John or the labrador is 18. It's better to separate the age statement into its own sentence, as it is a separate thought, or to simply avoid the use of the possessive noun form.