Search form can be added via Child Theme functions.php
file. Sample Child Theme can be downloaded from here.
First you need to add this code to Child Theme functions.php
file
// Custom Search in header via Child Theme functions.php
add_action( 'travelify_header', 'my_custom_search' , 5 );
function my_custom_search() {
get_search_form();
}
When you are done with that you will have to style this form and you can do by adding this Custom CSS to Theme Options - Other - Custom CSS or inside your Child Theme style.css
.searchform {
height: 30px;
z-index: 100;
float: right;
margin-top: 50px;
margin-right: 20px;
margin-left: 10px;
}
#branding input.s {
border: 1px solid #D0D0D0;
width: 120px;
text-indent: 10px;
padding-left: 10px;
}
Let me know if this helps.