I believe I have discovered a bug in the latest version of VLC for iOS (2.7.2 All Along the Watchtower) relating to the Plex DLNA server.
I use the Plex Media Server to host my music locally and use VLC for iOS to cache it for listening when I don't have an internet connection. When I am connected to my local network, VLC shows my Plex server under "Universal Plug'n'Play (UPnP)" in the Local Network view. I can browse my music collection as I would expect, and VLC offers download arrows next to the media items. However, when I use a VPN to connect to my server, the VPN does not route the UPnP broadcast packets, so I have to tell VLC to directly connect to the server using the "Connect to Server" option. After filling in the appropriate address and selecting "PLEX" from the button bar, I can connect and browse just as before, but there are no download buttons next to any media items.
I have managed to work around this problem by telling the Plex DLNA server to also broadcast UPnP packets on the VPN interface, but this seems like unintended behavior in VLC, so I brought it up here.