You can use the job id created by job generation POST to check the status of the reporting job and download the job when finished. Please note, that this API is not intended for public consumption so there is no documentation and the API can have breaking changes between minor kibana release.
To view the API in action, generate a report and go to the Kibana management->reporting. Open up your browser's network tab and view the XHR requests between the page and Kibana server.