Moomin

//Basically just copy+pasted your code and changed the field name to "my_countries" which it's called in AFC

unction my_searchwp_extra_metadata( $extra_meta, $post_being_indexed ) {
    
    // available author meta: http://codex.wordpress.org/Function_Reference/get_the_author_meta
    
    // retrieve the author's name(s)

    $author_country      = get_field('my_countries', $post_being_indexed->post_author );


    
    // index the author name and bio with each post
    $extra_meta['my_author_meta_country']     = $author_country;

    
    return $extra_meta;
}

add_filter( 'searchwp_extra_metadata', 'my_searchwp_extra_metadata', 10, 2 );

function my_searchwp_author_meta_keys( $keys )
{
    // the keys we used to store author meta (see https://gist.github.com/jchristopher/8558947 for more info)
    $my_custom_author_meta_keys = array( 
        'my_author_meta_country' 
    );
    
    // merge my custom meta keys with the existing keys
    $keys = array_merge( $keys, $my_custom_author_meta_keys );
    
    // make sure there aren't any duplicates
    $keys = array_unique( $keys );
    
    return $keys;
}
 
add_filter( 'searchwp_custom_field_keys', 'my_searchwp_author_meta_keys', 10, 1 );

//Var_dump

array(3) { [0]=> string(7) "Belarus" [1]=> string(5) "Italy" [2]=> string(5) "Japan" }