Flare's search engine behaves in a way that Google Analytics doesn't expect. Most search engines use a URL query to perform a search, but Flare's engine uses hashes. It's easy enough to add Google Analytics to an HTML output, but if you want to track your user's search terms, you have to do a tiny bit more work.
And you're done. Now you can get analytical information about how your users use your help, AND you can track which search terms they're using which allows you to make the improvements your users need!
This solution was developed with the help of Paul Pehrson, owner of DocGuy Training and a certified MadCap Flare trainer.