See documentation here too:
https://kriesi.at/documentation/enfold/social-share-buttons/#how-to-add-custom-social-icons-to-enfold-options

if there are not too many individual social icons, I would recommend not to use font icons, but to use images (png’s) instead
For this you would have to find a suitable image file for the icon – e.g.:
the whole thing is possible as circle too:

To Register the new Icon on Enfold put this to your child-theme functions.php

function avia_add_custom_social_icon($icons) {
	$icons['Kununu'] = 'kununu';
    return $icons;
}
add_filter('avf_social_icons_options','avia_add_custom_social_icon', 10, 1);

Now you can add on Enfold-Child Options – Social Profiles – the new icon ( it is at the end of the list : link maybe: https://www.kununu.com/ )

to have now the image for that new icon
you had to place this to your quick css
(the image dimensions depends on your other settings for social media icons – standard seem to be 30px):

#top #wrap_all .av-social-link-kununu a:before{
    content: "";
    width: 30px;
    height: 30px;
    float: none !important;
    display: inline-block !important;
    vertical-align: middle;
    background: url(PATH-TO-YOUR-IMAGE/kununu-quad.png) no-repeat center center;
    background-size: contain;
}

/**** hover style - just an example - if you make the image a bit smaller - you can style background-color ***/
#top #wrap_all .av-social-link-kununu:hover a {
-webkit-filter: hue-rotate(180deg);
filter: hue-rotate(180deg)
}

see here in my footer the example: https://webers-testseite.de/#footer

a bit offtopic but sometimes it is nice to use instead an image. You can use exactly the same code-snippet to register a new social share icon but with images ( png’s f.e.)
see documentation: https://kriesi.at/documentation/enfold/social-share-buttons/#gist85414748

see here in my footer the usage of png file: https://webers-testseite.de/#footer

___________________________________

PS : entypo-fontello ( standard Enfold font icon set has that little paper-airplane too) :

function avia_add_custom_icon($icons) {
    $icons['telegram']  = array( 'font' =>'entypo-fontello', 'icon' => 'ue8b7');
    return $icons;
}
add_filter('avf_default_icons','avia_add_custom_icon', 10, 1);

function avia_add_custom_social_icon($icons) {
    $icons['Telegram'] = 'telegram';
    return $icons;
}
add_filter('avf_social_icons_options','avia_add_custom_social_icon', 10, 1);

so it is not so easy but because on functions-enfold.php the ajax search function is a “pluggable function” you can have here a child-theme solution. Otherwise you had to have a complete functions-enfold.php in your child.
Every function surrounded by:

 if(!function_exists('…')){
…
}

can be substituted by child-theme function with same name! – because child-theme functions are loaded first – when it comes to the function with the same name in parent theme it does not load the parent function ( because of the if not exists clause)

i have edited that function (on base of enfold 4.7.3) and you can copy & paste that part to your child-theme functions.php

add_action( 'wp_ajax_avia_ajax_search', 'avia_ajax_search' );
add_action( 'wp_ajax_nopriv_avia_ajax_search', 'avia_ajax_search' );

function avia_ajax_search()
{
    global $avia_config;
	
    unset($_REQUEST['action']);
    if(empty($_REQUEST['s'])) $_REQUEST['s'] = array_shift(array_values($_REQUEST));
	if(empty($_REQUEST['s'])) die();

    $defaults = array('numberposts' => 5, 'post_type' => 'any', 'post_status' => 'publish', 'post_password' => '', 'suppress_filters' => false, 'results_hide_fields' => '');

    $_REQUEST['s'] = apply_filters( 'get_search_query', $_REQUEST['s']);

    $search_parameters 	= array_merge($defaults, $_REQUEST);

    if ( $search_parameters['results_hide_fields'] !== '' ) {
        $search_parameters['results_hide_fields'] = explode(',', $_REQUEST['results_hide_fields']);
    }
    else {
        $search_parameters['results_hide_fields'] = array();
    }

    $search_query 		= apply_filters('avf_ajax_search_query', http_build_query($search_parameters));
    $query_function     = apply_filters('avf_ajax_search_function', 'get_posts', $search_query, $search_parameters, $defaults);
    $posts		= (($query_function == 'get_posts') || !function_exists($query_function))  ? get_posts($search_query) : $query_function($search_query, $search_parameters, $defaults);

    $search_messages = array(
            'no_criteria_matched' => __("Sorry, no posts matched your criteria", 'avia_framework'),
            'another_search_term' => __("Please try another search term", 'avia_framework'),
            'time_format'         => get_option('date_format'),
            'all_results_query'   => http_build_query($_REQUEST),
            'all_results_link'    => home_url('?' . http_build_query($_REQUEST)),
            'view_all_results'    => __('View all results','avia_framework')
        );
	
    $search_messages = apply_filters('avf_ajax_search_messages', $search_messages, $search_query);
	
    if(empty($posts))
    {
        $output  = "<span class='av_ajax_search_entry ajax_not_found'>";
        $output .= "<span class='av_ajax_search_image ".av_icon_string('info')."'>";
        $output .= "</span>";
        $output .= "<span class='av_ajax_search_content'>";
        $output .= "<span class='av_ajax_search_title'>";
        $output .= $search_messages['no_criteria_matched'];
        $output .= "</span>";
        $output .= "<span class='ajax_search_excerpt'>";
        $output .= $search_messages['another_search_term'];
        $output .= "</span>";
        $output .= "</span>";
        $output .= "</span>";
        echo $output;
        die();
    }

    //if we got posts resort them by post type
    $output = "";
    $sorted = array();
    $post_type_obj = array();
    foreach($posts as $post)
    {
        $sorted[$post->post_type][] = $post;
        if(empty($post_type_obj[$post->post_type]))
        {
            $post_type_obj[$post->post_type] = get_post_type_object($post->post_type);
        }
    }

    //now we got everything we need to preapre the output
    foreach($sorted as $key => $post_type)
    {

        // check if post titles are in the hidden fields list
        if ( ! in_array('post_titles', $search_parameters['results_hide_fields'] ) )
        {
            if(isset($post_type_obj[$key]->labels->name))
            {
                $label = apply_filters('avf_ajax_search_label_names', $post_type_obj[$key]->labels->name);
                $output .= "<h4>".$label."</h4>";
            }
            else
            {
                $output .= "<hr />";
            }
        }

        foreach($post_type as $post) {

            $image = "";
            $extra_class = "";

            // check if image is in the hidden fields list
            if (!in_array('image', $search_parameters['results_hide_fields']))
            {
                $image = get_the_post_thumbnail($post->ID, 'thumbnail');
                $extra_class = $image ? "with_image" : "";
                $post_type = $image ? "" : ( get_post_format($post->ID) != "" ? get_post_format($post->ID) : "standard" );
                $iconfont = $image ? "" : av_icon_string($post_type);

            }

            $excerpt     	= "";

            // two new lines here
            $the_id 		= $post->ID;
			$commentCount 	= get_comments_number($the_id);

            // check if post meta fields are in the hidden fields list
            if ( ! in_array('meta', $search_parameters['results_hide_fields'] ) )
            {
                if(!empty($post->post_excerpt))
                {
                    $excerpt =  apply_filters( 'avf_ajax_search_excerpt', avia_backend_truncate($post->post_excerpt,70," ","...", true, '', true) );
                    
                    $excerpt .= "<br class='linebreak'/><span>".get_the_time( $search_messages['time_format'], $post->ID )."</span>";
                    
                    if ( $commentCount != "0" || comments_open($the_id) && $entry->post_type != 'portfolio')
					{
						$link_add = $commentCount === "0" ? "#respond" : "#comments";
						$text_add = $commentCount === "1" ? __('Comment', 'avia_framework' ) : __('Comments', 'avia_framework' );

						$excerpt .= "<span class='sep'>&nbsp;/&nbsp;</span><span>{$commentCount} {$text_add}</span>";
					}
                }
                else
                {
                    $excerpt = apply_filters( 'avf_ajax_search_no_excerpt', get_the_time( $search_messages['time_format'], $post->ID ), $post );

                    if ( $commentCount != "0" || comments_open($the_id) && $entry->post_type != 'portfolio')
					{
						$link_add = $commentCount === "0" ? "#respond" : "#comments";
						$text_add = $commentCount === "1" ? __('Comment', 'avia_framework' ) : __('Comments', 'avia_framework' );

						$excerpt .= "<span class='sep'>&nbsp;/&nbsp;</span><span>{$commentCount} {$text_add}</span>";
					}
                }
            }

            $link = apply_filters('av_custom_url', get_permalink($post->ID), $post);

            $output .= "<a class ='av_ajax_search_entry {$extra_class}' href='".$link."'>";

            if ($image !== "" || $iconfont) {
                $output .= "<span class='av_ajax_search_image' {$iconfont}>";
                $output .= $image;
                $output .= "</span>";
            }
            $output .= "<span class='av_ajax_search_content'>";
            $output .= "    <span class='av_ajax_search_title'>";
            $output .=      get_the_title($post->ID);
            $output .= "    </span>";
            if ($excerpt !== '') {
                $output .= "    <span class='ajax_search_excerpt'>";
                $output .=      $excerpt;
                $output .= "    </span>";
            }
            $output .= "</span>";
            $output .= "</a>";
        }
    }

    $output .= "<a class='av_ajax_search_entry av_ajax_search_entry_view_all' href='".$search_messages['all_results_link']."'>".$search_messages['view_all_results']."</a>";

    echo $output;
    die();
}

because there was a css rule in enfold that sets the breaks in ajax search to display:none
you had to put this in additon to quick css

#top #searchform br.linebreak {
    display: block;
}

you can test it here on my playground – put in search : buttons
https://webers-testseite.de/