It is currently not possible to retrieve reports from a service desk project using the REST APIs for JIRA Service Desk.
When clicking on a report (e.g. customers' satisfaction), I can see (in the developers' tools console) that the endpoint "/rest/servicedesk/SERVICEDESK-ID/projects/PROJECT-KEY/report/REPORT-NAME" is called.
Using the above url in the browser address bar displays the desired results. This endpoint should also be available to be consumed using REST calls.
You can use curl and call (change the limit according to your needs):
NOTE: this is not an optimal solution since this is only used internally and it may change without notice. Refer to Latest JIRA Service Desk REST API Reference for changes to structure