SQL Server High Availability without Windows Clustering
As per my understanding and information, there isn't any SQL Server High Availability(HA) feature without Windows Server Failover Clustering mechanism (WSFC) being used.


Correct.


  SQL Server Mirroring used to be one such option where HA was possible without WSFC but with Microsoft stating that Mirroring would be removed soon from the product


Also correct.


  One of the updates in vNext was that Microsoft would be releasing an option for Cluster Free Availability groups.


Correct, but this does NOT provide HA, so you will still need to use cluster for HA even in vNext.


  But as of now, do we have any Cluster Free HA feature within the product(SQL Server 2012, 2014, 2016)?


Mirroring. If you can setup mirroring you can setup clustering and use AGs - I'm not sure why the big push to not have to use Windows Clustering.