Representing a Kibana query in a REST, curl form

At the bottom of your visualization, there is a small caret you can click in order to view more details about the underlying query:

Then you can click on the "Request" button in order to view the underlying query, which you can copy/paste and do whatever suits you with it.

UPDATE

Then you can copy/paste the query from the "Request" textarea and simply paste it in a curl like this:

curl -XPOST localhost:9200/your_index/your_type/_search -d '{
  "query": {
    "filtered": {
      "query": {
        "query_string": {
          "analyze_wildcard": true,
          "query": "blablabla AND blablabla"
        }
      },
      "filter": {
        "bool": {
          "must": [
            {
              "range": {
                "@timestamp": {
                  "gte": 1439762400000,
                  "lte": 1439848799999
                }
              }
            }
          ],
          "must_not": []
        }
      }
    }
  },
  "highlight": {
    "pre_tags": [
      "@kibana-highlighted-field@"
    ],
    "post_tags": [
      "@/kibana-highlighted-field@"
    ],
    "fields": {
      "*": {}
    }
  },
  "size": 420,
  "sort": {
    "@timestamp": "desc"
  },
  "aggs": {
    "2": {
      "date_histogram": {
        "field": "@timestamp",
        "interval": "30m",
        "pre_zone": "+02:00",
        "pre_zone_adjust_large_interval": true,
        "min_doc_count": 0,
        "extended_bounds": {
          "min": 1439762400000,
          "max": 1439848799999
        }
      }
    }
  },
  "fields": [
    "*",
    "_source"
  ],
  "script_fields": {},
  "fielddata_fields": [
    "@timestamp"
  ]
}'

You may need to tweak a few stuff (like pre/post highlight tags, etc)

Another option would be to query Elastic Search using lucene queries (same syntax Kibana uses) using the ES search API query_string queries:

https://www.elastic.co/guide/en/elasticsearch/reference/current/query-dsl-query-string-query.html

Taken from one of the doc example, you would query ES using something like this:

GET /_search
{
    "query": {
        "query_string" : {
            "default_field" : "content",
            "query" : "this AND that OR thus"
        }
    }
}

In case you are online using a Chrome browser you can go to your Kibana dashboard, open the developer console and write your query while having the Network tab open in the developer console. When you search for your query in the Kibana dashboard you will see the request appear in the developer console. There you can "right click" and select Copy as cURL, which will copy the curl command to your clipboard. Note that credentials of your basic auth may be copied as well. So be careful where you paste it.