Chrome has to run Flash how Flash wants to be run, because doing otherwise could cause massive problems with any plugin. This is part of why it took so long for them to make Chrome, resolving the memory independence desires with the needs of plugins requires giving some things up. It was either roughly all plugins in existence, or allow the same process to interact with multiple tabs / windows.
Heck, Firefox uses a lock-file in your profile to prevent multiple instances from running. What's to stop a plugin from requiring such a file, writing / reading it frequently, and having no error handling because it's only designed to run singly? Ultimately, you either harden the separations to run multiple instances of it, breaking many in the process and possibly damaging data irrecoverably, or you just let the plugin decide and have backwards compatibility, which is hugely important for a browser.
You can see your flash cookies at this website:
http://www.macromedia.com/support/documentation/en/flashplay...
You'll notice that they are the same no matter what browser you use.