Own permissions

This is doable with a bit of custom code, adapt as needed - in my case I didn't care about specific permissions, just entity ownership:

/**
 * Implements hook_entity_info_alter().
 */
function MODULE_entity_info_alter(&$entity_info) {
  $entity_info['ENTITY']['access callback'] = 'MODULE_ENTITY_access';
}

/**
 * Entity access callback.
 */
function MODULE_ENTITY_access($op, $entity, $account, $entity_type) {
  switch ($op) {
    case 'view':
    case 'update':
    case 'delete':
      if ($entity->uid == $GLOBALS['user']->uid) {
        return TRUE;
      }
      break;
  }

  return eck__entity_access($op, $entity, $account, $entity_type);
}

Weirdly, ECK seems to halfway offer 'own' management functionality. When the $b_own argument for eck__multiple_access_check() is set to TRUE, for each permission in the passed-in array, it also checks for one with the same name appended with " own". So for example, if a menu callback was checking for "eck administer my_type my_bundle entities" and "eck edit my_type my_bundle entities", it would also check "eck administer my_type my_bundle entities own" and "eck edit my_type my_bundle entities own".

But, ECK itself doesn't actually declare those '... own' permissions in hook_permission, and I've not found anywhere that actually uses $b_own = TRUE, so I guess it never got fully implemented (or is a vestige of an earlier 'own' permission model).