I've put together a functional test of some code I'm working on to automatically download and install the flash plugin for Firefox Portable. It's simple yet seems to work quite well even with many proxies as long as they are properly defined in IE/Windows and doesn't leave anything behind.
When run, it'll download the plugin from Adobe's server and install it into your copy of Firefox. You just select your FirefoxPortable directory in the installer and it does the rest. Please give it a try and let me know if it works for you. If not, please provide details (your OS, directory installed to, error message received, etc).
Download Flash Plugin for Firefox Portable 0.1 [120KB download / 2.8MB installed]
PORTABILITY NOTE: Adobe Flash is not portable and will store Local Shared Objects (aka Flash Cookies) on every PC you visit. Firefox does not have access to these and they are not deleted when you delete private data though you can use the Objection extension to view them.