Custom Color Schemes for WP 3.8?

You place your color scheme anywhere, just register it using wp_admin_css_color() and point $url to your location.

Okay, I know how to register it. Now which function can I use in functions.php to allow me to have the theme use a specific color scheme?

You could force all users to use a specific theme like this:

add_action( 'admin_init', function() {

	// check if current theme is "Twenty Fourteen"
	if ( wp_get_theme()->get( 'Name' ) == 'Twenty Fourteen' ) {

		// remove the color scheme picker
		remove_action( 'admin_color_scheme_picker', 'admin_color_scheme_picker' );

		// force all users to use the "Ectoplasm" color scheme
		add_filter( 'get_user_option_admin_color', function() {
			return 'ectoplasm';
		});

	}

});