this seems more like a Logstash question than an Elasticsearch one...
I have not done anything like what you are looking to do but I'm going to reply anyway
There does not seem to be an sql input plugin for Logstash https://www.elastic.co/guide/en/logstash/current/input-plugins.html
With my limited knowledge I would write a script that would pull out the data you want from SQL and export as JSON. Filebeat or Logstash could then take that JSON and index it in ES. Or ship directly to ES... I would suggest using Logstash or Filebeat as they handle some errors and log quite well if there are issues.