Color schemes are registered globally within $_wp_admin_css_colors (see wp-includes/general-template.php for reference).
You can return the colors for the current user depending on get_user_meta() for a specific settings page like this:
global $pagenow;
if ( $pagenow == 'options-permalink.php' ) :
add_action( 'admin_notices', 'get_current_user_admin_color' );
function get_current_user_admin_color() {
global $_wp_admin_css_colors;
$user_admin_color = get_user_meta(get_current_user_id(), 'admin_color', true);
echo '<pre>';
var_dump($_wp_admin_css_colors[$user_admin_color]->colors);
echo '</pre>';
}
endif;
Feel free to vary the action hook to fit your needs: maybe admin_notices is to specific, so you may also try something like admin_head.
Moreover $_wp_admin_css_colors[$user_admin_color] is holding even more meta data about the current admin color scheme:
[name]Name of the current admin color scheme[url]Absolute path to the current color scheme CSS file[colors]Colors of the current admin color scheme[icon_colors]Icon colors of the current admin color scheme