You cannot download "through" an existing session.
sftp work by creating new sessions and talking to an executable on the other end that's running in place of a shell.
The main problem I have is that said file is under root on the server so doing a sftp command is not that simple.
You are logged into a remote server. I presume you can get to this file under your non-root account. So,
scp should work. The user your specify under
scp can reach everything as if you were logged in.
If you are needing to
su to get to this file on the remote system, the proper thing to do is copy it to your normal user's home directory,
chmod so your normal user owns and can read it, then get it with
scp, etc. If the file is very large,
chmod the file directly temporarily without making a copy.
Another thing you can try - If you are running your own SSH server at home or wherever, and it's reachable from the remote SSH server you're logged into, you can use
scp to send it from your remote session to your local system.