From what I can see, you need to run the Selenium server in background (and terminate it at the end) so that you can do something else while it’s running.
It’s probably best to find a sample/tutorial by someone who walked this road before. Travis doesn’t endorse or promote any particular ways of doing things beyond what the stock functionality provides.
Existing functionality for GUI and browser testing is described at https://docs.travis-ci.com/user/gui-and-headless-browsers/.