One way to copy the data is using rsync from the My Cloud SSH command line to copy the files from the My Cloud to the Synology NAS. See the following post where I explained (in general terms) how I used rsync to copy from a My Cloud to a Synology NAS running DSM 7.x.
One can incorporate the nohup command with the rsync command which will allow one to close the SSH terminal while the rsync continues to run on the My Cloud.
If one needs a DLNA media server (similar to Twonky) on Synology one can either enable the DLNA server option within the Plex Media Server Settings or they can install the Media Server package from the Synology DSM Package Center.
How to enjoy multimedia contents stored on Synology NAS with DLNA/UPnP-compliant DMAs?
Plex’s DLNA media server:
