Read up online on “how to copy a Flash game save file”. This is just once source >>> https://itstillworks.com/12390875/how-to-transfer-flash-game-saves
If you are not using your own computer then you my not have access to the saves files IF that computer shops computer even stores online saves at all.
You may have to “convince” the owner to allow you to keep your game saves on the PC that you play from or to use some sort of save medium like a Stick to transfer the save file each time you play.
Hope this helps.
p.s. About downloading Flash games. Once the game has been loaded into your device you do not need to be online anymore.
You can keep playing it as long as you keep the game open in the browser that you are using.
For more info read up on help sites for Browser Flash Games. They help. 😉