Each local dungeon consists of two separate files: a screenshot and a dungeon file. Both files can be found in the same directory:
Windows:
C:\Users\USERNAME\AppData\LocalLow\FIRECHICK\SuperDungeonMaker\LocalDungeons\macOS:
~/Library/Application Support/FIRECHICK/SuperDungeonMaker/LocalDungeons/
The files have the same name, with the dungeon file having the suffix "_dungeon.dgn" and the screenshot file having the suffix "_preview.png".