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They are not saved automatically. You have to take action to save them. There are several ways. They originate with the buttons on the top right of an image:

 The right one, "favourite", saves them in the local browser cache. This method allows you to go back and see the image and the prompts and styles that created it. The favourites are only available in that browser on that computer, and can be lost if you delete local browser data. You can see any favourites saved from the "Favourites" tab on the main Firefly page (this example is from a mobile phone):

The button on the left provides several options:

• Download allows you to save the image to your local computer
• Share a link allows to to copy a URL that takes you back to the image in firefly where you can see the prompt and styles 
• Copy image allows you to paste the image into another application
• Save to library allows to save a copy of the image to your Creative Cloud library (and access from other Adobe products)

If you do not save via one of these, the image is lost forever.