They are not being stored on the LS host unless you've configured it to output to stdout for debugging or configure it to do otherwise. The LS host should be parsing and filtering the logs its getting from filebeat and pushing them to ES as fast as it can filter and process them. The logs are then stored in ES in the indexes you've specified if my understanding of LS is not faulty in this matter.
I assume from your reply you got the filebeat -> logstash -> elasticsearch working. I didn't see any reply to your other topic.