Can I transfer files between two remote servers with WinSCP?

To transfer files between the two servers via local workstation

See documentation to learn how to duplicate files between sessions.

This feature is not built into WinSCP, for reasons listed further down. Yet, there are ways to utilize some advanced feature

With SFTP and SCP protocols, you can push the selected remote files to another server using scp custom command.

With SFTP and SCP protocols, you can use suitable remote command to download files to the remote server from another server. E.g.:

wget ftp://username:password@otherhost:/path/file ./

SFTP protocol does not allow this.
With SCP protocol it may be theoretically possible. However it has many drawbacks. It would require not only major changes in WinSCP, but also many configuration changes on both servers to allow authenticate on the second server from the first one (note that it would not be possible to use password authentication). See scp custom command for details. So practically it would have advantage for advanced users only, who can use the “custom command” solution easily.
For FTP protocol has an FXP extension that allows this, but it is not supported by WinSCP. 309