I don't have any iOS devices, but in my comment I recommended a specific piece of software ("Syncthing" is the actual name), and I can assure you it works well on the other operating systems you listed, as well as Android.
If you want to edit the file in multiple places, I think Syncthing is pretty much the best option there is. If you plan to do all edits at the same device but just want to view it elsewhere, something like regularly copying the file to the others with rsync or sftp or whatever your preference is may be enough. I manage some files in syncthing while others are just backed up to a server regularly with rsync. The downside of the one-way copying approach is that you may end up with an old version on some machines at some point, or if you suddenly do want/need to edit on a different device, you then have two versions of the file to deal with. Syncthing is kinda like Dropbox, but it's free software and decentralized. I think it uses bittorrent to copy things between your devices. If you consider yourself forgetful, a more automated/background solution like Syncthing also has benefits over manually copying stuff. You can just read/edit your file as normal and it'll sync so long as the daemon is running.