That's right, casting isn't available from either of our iOS clients for the time being. If your server is local, you can use the DLNA function in VLC to access your server and also Cast, or use Infuse's cast ability as well.
If the Chromecast is a newer one with a remote (Chromecast with Google TV), then just install our Jellyfin for Android TV app from the Play Store.
For Fintunes, it's worth asking where you downloaded it from. Was it F-Droid?
I'm part of the Jellyfin Core Team, and for our own official app, the normal one (sideloaded APK or Google Play) has Cast support, while the F-android version doesn't. It's because Casting relies on a Google proprietary SDK module.