The save file for Potioneer is stored in your AppData folder. You may need to enable hidden files and folders in File Explorer in order to see them.

C:\Users\<your-username>\AppData\LocalLow\Focus on Fun Games\Potioneer

Though the Linux version of the game hasn't been released yet, it is planned before Early Access is done. The save file for Potioneer will be stored in the ~/.config/unity3d/FocusOnFunGames/Potioneer directory.