Styling the Check Out flow is easy - you don't have to do much. All elements in the Check Out flow automatically inherit styling from the global text styles. If you use a template all texts will be styled and customized beforehand, and therefore the Check Out flow will as well.
If you make global text changes, the Check Out flow will automatically inherit the new text styling, so you don't have to do anything, and you assure a coherent design all over your site.
Overview: Normal page vs. Check Out page