It's not something you can readily do.
The form on this page: hidden link
You want the fields for surname, first name, date of birth etc. to be auto-filled, yes?
When you add fields to a Form you can include the value attribute to provide an initial default value.
If you had, say, user fields with the relevant data then you could use these types fields as the default values (when editing the form add a value="" attribute to a field and then use the Fields and Views button to insert a shortcode for the corresponding user field for the current user).
But you can only supply one default value, such as a user field for the current user.
It would be possible to add an id attribute to the shortcode which produces the user field to output the field value from a different user, not the current user.
So, in theory, if all the family members had user accounts you could populate the form with default values that came from different users.
But that would have to be determined at the time the form was generated (by—somehow—setting the id of the desired user).
What is not possible is for that form to be shown on the screen and *then* the user selecting another user (family member) whose details should be used to populate the form, by the time the form is rendered it is too late to change default values.
Now, I've been describing doing this with different users.
But you say you want to add family members without creating new users.
You could add a custom post type for the family members with fields for each, and you could then set up the form to populate the value attributes with fields from one of the child posts which you would have to set at the point the form was rendered. (The user, e.g. the father, would have to add one of the same child posts for themselves so that it would be possible to pre-populate the form with their field values.)
I'm not going in to too much detail here because I suspect this is not what you want, having to know whose details should be used before the form is even rendered.
