Well, what you’re trying to do probably won’t be easy. I’d recommend just using a screenshot and a color picker tool to get the colors. If you really want to go through the trouble of inspecting XUL documents, it’s possible, of course.
You need the DOM Inspector extension installed. With dev tools open, launch the DOM Inspector and inspect the chrome://browser/content/devtools/framework/toolbox.xul chrome document. The document selection is available in the menu bar.
DOM Inspector isn’t very comfortable, but has roughly the same feature-set as the DOM view in the native dev tools.