How to add search bar in header for Travelify WordPress theme?

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.