You can run jSuneido (the Java version) on Linux, but it does not have any GUI. The user interface is only available with cSuneido on Windows.
You can run jSuneido as server on Linux and connect to it from cSuneido clients running on Windows.
Or if you are using jSuneido as a web server, that will run fine on Linux.
People have tried running cSuneido on Linux using Wine but I think there were issues with this. I don’t know if anyone has tried lately.