No. I mean, the game developer would have to implement that. Flash Player is a language runtime. It's not a video game engine or something. We just run the code that the developer writes and do the low-level work of drawing pixels and making sounds, etc.
The game probably saves content in a Local Shared Object (LSO), which is Flash Player's equivalent to a cookie. Whenever you clear your browser cache, or if those files otherwise get deleted/corrupted, that data goes away. The LSOs are stored in a specific folder, which you could theoretically make regular backups of.
If you were building a game and wanted that data to be stored in a resilient way, you'd probably keep a copy on the users's computer so that it could access it quickly, but stash a backup on a server in case it ever went missing (or create some scheme that allows you to encode all the game data in a code, etc.).
Anyway, if you want to get deep into it, the System Administrator's Guide has details on where that folder lives for various operating systems. You'd want to make sure your backup software is making regular backups of it (and probably keeping multiple versions), and if you need to restore it, you'd need to know where to look for it.
https://www.adobe.com/devnet/flashplayer/articles/flash_player_admin_guide.html