You can't.
Private Browsing mode means that Firefox doesn't store data to disk (cookies and local storage) and this is also respected by plugins like Flash.

You will have to revert from using PB mode to be able to keep the volume setting and other settings.

Thank you.

In previous versions of Adobe Flash, data was stored even in PB. Are you sure there isn't any workaround?

I appreciate your help.

Not that I know of.
You are also on Windows XP and that platform only has one global volume setting for all applications and not a setting per application like later Windows versions have.

Thanks again.

You're welcome