If it's a movie blu ray you can usually play the "index.bdmv" file in a compatible media player e.g. VLC definitely works. MPC-HC / MPC-BE works too, I think(?) MPV can play them too. As well as Jellyfin and Kodi if that's your thing.
Alternatively browse into the "STREAM" folder, usually the biggest .m2ts file in there is the actual movie or whatever it is you want to play. The above media players can play that directly if preferred.
For TV series the above usually works too but the episodes are usually split out among multiple .m2ts files so it might be easier just to play them directly in that case.
Except that it wouldn't. The infohash that the private flagged torrent generated is different vs a public non-private torrent of the same contents. Your suggestion would purposely share the same exact private torrent infohash into public DHT/PEX, that would certainly get people banned at the source private tracker(s). I also suspect most/all torrent client developers would consider that incorrect behavior.
If you wanted to do a more "correct" approach on this - Create a brand new public non-private flagged torrent of those contents, which would generate its own unique infohash, then it's just a regular torrent. You'd end up needing to seed multiple copies of the same torrent (the original private flagged torrent and your new public torrent) but sure that would be possible as long as the torrent client itself has DHT/PEX enabled. Most private trackers won't care too much but some of that does depend on individual trackers and uploaders, you'd need to check their rules.