You mentioned the "most efficient way" - do you need to do bulk export? In that case, exporting to a cloud storage bucket is the most efficient way.
If you just want to dump query result to file, assuming the number of rows is small, you can use the command line tool and pipe the result to a file (https://developers.google.com/cloud-sql/docs/commandline). SQuirreL SQL should be able to do the same thing. Not sure about that particular error you got.