To be honest, I'm no big fan of using the default Bootstrap framework provided by Phoenix. The basic version isn't even the problem, it's just I think that Bootstrap-y sites look boring and all the same. There are so many frameworks out there, why don't use another one?
UIKit may be the simplest way to use another framework. Just download the zip from the UIKit website and unzip the content to web/static/vendor. Now the only thing's left is to include jQuery to your project. Install it as a dependency:
npm install jquery --save
And include jQuery in your brunch-config.js:
whitelist: ["phoenix", "phoenix_html", "jquery"]
That's it! An optional step is to delete all of the content from web/static/css/app.css (which includes Phoenix's Bootstrap CSS config).