It's a known problem and you can find a ticket here. I've faced the same issue while upgrading from 6.4.2 to 6.5.4 - so it's not fixed yet.
So, if you see in your logs something like this:
... Creating index .kibana_2.
... Reindexing .kibana to .kibana_1
... Another Kibana instance appears to be migrating the index. Waiting for that migration to complete. If no other Kibana instance is attempting migrations, you can get past this message by deleting index .kibana_2 and restarting Kibana.
and Kibana server is not ready yet in browser for a long time (more than 2 hours in my case) - it's waiting for your help. Just drop both these indices:
curl -XDELETE -H 'Content-Type: application/json' 'http://elasticsearch:9200/.kibana_2'
curl -XDELETE -H 'Content-Type: application/json' 'http://elasticsearch:9200/.kibana_1'
And don't forget to restart Kibana.
