In the terminal, to start Jekyll, navigate to your sites root folder and type jekyll build --watch. The root folder will be generated into ./_site and watched for changes with auto-regeneration enabled.

After you add your project to CodeKit, click on the gear under your project name to access your project settings.

Click the Browser Refreshing option. Add the _site folder as the Document-Root Subpath:

Set Refresh Delay to more than 0 seconds, I used the preset interval of 0.25 seconds. At 0 seconds, your markdown files will not reload initially. Adding this delay allows them time to build.

Screenshot