Portable Firefox for Mac
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/&lt;FLASHDRIVENAME&gt;/Firefox/Firefox.app/Contents/MacOS/firefox -profile /Volumes/&lt;FLASHDRIVENAME&gt;/Firefox/&lt;profile folder&gt;


If you execute 

$ bash /Volumes/&lt;FLASHDRIVENAME&gt;/Firefox/start.sh


You should be able to run Firefox on any Mac anywhere.

NOTE: Replace &lt; FLASHDRIVENAME > with the mountable name of your flash drive.