You’re close. In the #SharedObjects folder should be another folder with random numbers and letters. Click that and it’ll be full of a bunch of different websites. You want “chat.kongregate.com” – that folder has everything.
I’ve tried to search for #SharedObjects and I found this directory:
C:\Users\USER\AppData\Local\Google\Chrome\User Data\Default\Pepper Data\Shockwave Flash\WritableRoot\#SharedObjects\