I have just used the platform supported color picker widget in one of my apps. I like the widget a lot but it is turning out to be non-trivial to use the hex colors values stored in an attribute to actually color any elements (Buttons, backgrounds, etc.) in the app!
Other than targeting an element on the page with javascript, there is no way to color any elements on the page. There are a couple of community provided marketplace modules that allow dynamic hex values to color elements but it seems like if the platform publishes the color picker, there should be a built in way to utilize the colors selected with the widget.