Unfortunately, all the data is stored locally in the browser’s HTML Local Storage. I’d suggest just saving all your solutions (e.g. email them to yourself) and paste them in on your new device.
Creating an account system is something I’d like to do, but I was waiting to see if there was interest in the game first :)
Update: In the future, I'd like to use itch.io accounts and the itch.io app for "cloud saving" of solutions/settings. At the moment, however, there are a couple of blocking issues in the itch.io app (and the version of Electron the app uses). The bottom line is that this won't be available for quite some time, unfortunately.
