Programatically change user field (entity reference) in drupalgap with user_save()?
It depends largely on what Widget you have selected for your entity reference field on your Manage Display page. The easiest widget to work with is the Autocomplete widget, at which point you'd send up this JSON:

"field_checked_in_chargingstation": {
 "und": [
  {
   "target_id": "... (29088)"
  }
 ]
},


The Services module is coupled with the forms system in Drupal, so as you change the widget on a field, the JSON data you need to send to Drupal may change.