Did a quick poke around that target theme and I am thinking you are going to have to manually enter the "get search form" in the header file.
You may have to finagle the CSS to get the theme's searchform.php to dispaly properly in that top menu (that is where you want this, yes?)
Basically you will open your site and go to the admin section, click on "Appearance >> Editor" and in there choose the "Header (header.php)" file.
Scroll all the way to the bottom of that file and look for
Insert the get_search_form function between the /div and menu end, so it now looks like:
<?php get_search_form( $echo ); ?>
That "should" get you closer to what you are looking to do.