How to create a read-only flag that can only be used by an admin to actually flag nodes?
Try setup Flag as "global flag" and then in "Flag access" setup "Roles that may use this flag" check-boxes only for Admin.

If in this case flag will not be shown for other users - you need create script that get flag value for each node and display this info.

$flag = flag_get_flag(FLAG_NAME);
$node-&gt;flag_value = $flag-&gt;get_count($node-&gt;nid);