You want to push the documents separately, but you can do it in one request using elasticsearch's bulk API, https://www.elastic.co/guide/en/elasticsearch/reference/current/docs-bulk.html.
With that said, if you want to export the exact same kibana settings to several servers using a reindex is another option, https://www.elastic.co/guide/en/elasticsearch/reference/current/docs-reindex.html#reindex-from-remote.
You will need to imports mappings if you're configuring these servers before Kibana starts. If kibana starts first then it'll push mappings up to the .kibana index (which happens on startup if it doesn't exist).