One thing I m not able to get is how is what call is it making to get the query results. It seems it's using some websockets

You can use

fleetctl --help

to get details of how to use the command line. I believe you're right that it does use websockets - if your fleet server(s) is(are) behind a load balancer you need to make sure the LB works with websockets.

But I need to interact with my Kolide Fleet instance with api