There's no way in-game in this version, 0.56.3; the next public version (current patron version) adds Ren'Py Sync, which would let you transfer the saves to another platform, including web.
That said, the save files are stored on the phone (maybe in the SD card) at: Android\data\com.phanes.ruinme\files\saves
Backing up the files in that directory (using a computer) and restoring them when you reinstall should restore your saves, but do so at your own risk.