By default, Flatsome only displays shop result for its search page. To integrate Relevanssi into Flatsome, we need to add the below code to child theme function.php:

remove_action( 'woocommerce_after_main_content', 'flatsome_pages_in_search_results', 10 );
// Add Pages and blog posts to top of search results if set.
function relevanssi_pages_in_search_results() {
if ( ! is_search() || ! get_theme_mod( 'search_result', 1 ) ) {
return;
}
global $post;
if ( get_search_query() ) {
$args = array(
'post_type' => 'post',
's' => get_search_query(),
);
$query = new WP_Query();
		$query->parse_query( $args );
		relevanssi_do_query( $query );
		$posts = array();
		while ( $query->have_posts() ) {
			$query->the_post();
			array_push( $posts, $post->ID );
		}
		$args = array(
			'post_type' => 'page',
			's'         => get_search_query(),
		);
		$query = new WP_Query();
		$query->parse_query( $args );
		relevanssi_do_query( $query );
		$pages = array();
		while ( $query->have_posts() ) {
			$query->the_post();
			$wc_page = false;
			if ( 'page' === $post->post_type ) {
				foreach ( array( 'shop', 'cart', 'checkout', 'view_order', 'terms' ) as $wc_page_type ) {
					if ( $post->ID === wc_get_page_id( $wc_page_type ) ) {
						$wc_page = true;
					}
				}
			}
			if ( ! $wc_page ) {
				array_push( $pages, $post->ID );
			}
		}
		do_action( 'flatsome_products_page_loader' );
                if ( ! empty( $posts ) || ! empty( $pages ) ) {
                     $list_type = get_theme_mod( 'search_result_style', 'slider' );
                     if ( ! empty( $posts ) ) {    
		            
                             
add_action( 'woocommerce_after_main_content', 'relevanssi_pages_in_search_results', 10 );

Full code: ref: https://www.relevanssi.com/knowledge-base/flatsome-theme-product-search-results-page/