You cannot add Commerce Kickstart to an existing Drupal 7 website. Installation profiles / distributions are only used to create new sites, not enrich existing sites. This is the general Drupal pattern of things, not something specific to Commerce Kickstart. However, since the distribution is built using freely available modules on drupal.org, you can just find the specific modules you want and add them to your normal modules directory.

A lot of folks start with the Shiny theme and the Backoffice module.