While I have written a portable version of Google Chrome for Windows, Chrome and Firefox have similar file structure, I'll give this semi tutorial a go..
First, copy your /Applications/Firefox.app to a folder named "Firefox" on a flash drive.
Now, locate a valid user profile for Firefox on your Mac (usually ~/Library/Mozilla/Firefox/Profiles/ or ~/Library/Application Support/Firefox/Profiles/ )
Copy a valid profile folder to this "Firefox" folder also.
Next, we will create a Bash script to properly open Portable Firefox, so..
Inside this "Firefox" folder create a "start.sh" with the following lines:
/Volumes/<FLASHDRIVENAME>/Firefox/Firefox.app/Contents/MacOS/firefox -profile /Volumes/<FLASHDRIVENAME>/Firefox/<profile folder>
If you execute
$ bash /Volumes/<FLASHDRIVENAME>/Firefox/start.sh
You should be able to run Firefox on any Mac anywhere.
NOTE: Replace < FLASHDRIVENAME > with the mountable name of your flash drive.
The version Firefox v22 for Mac at http://portableapps.com/node/37665 is stable.
I use it and it works great.