Member Identification Card
Apologies. This is a Drupal answer and I know you are on Wordpress, but this ticket might attract drupal users too so thought I would outline the approach.
There is a View you can download here which provides the logged in user a block with their Membership status etc, and this could be modified to include other fields including image. Using the Print module, or Views PDF this could then have a download option for the user to 'take it away'.