How to add flag on each field in a node in Drupal?
I am gonna say something different than @Volker, hopefully correct.

Important: You need to install the File Entity module to allow flags on your image field's multiple values.

Just tried this and it works for me, using:


A multivalued Image field; setting its display "Format" to "Rendered file" and the "View mode" to "Teaser", here is a screenshot of my configuration:

A new Flag for File entities; selecting the respective "Display in entity links" view modes. Selecting is optional, it should work out of the box.


And there is what I get:



Hope this helps!