BuddyPress.org

Codex reference:

Members Navigation Menus

Also, on the forum, several topics, with many snippets:
https://buddypress.org/support/search/bp_nav_menu/

Here a working example, which add 2 external links on a profile.

function bpfr_custom_setup_nav() {
  if ( bp_is_active( 'xprofile' ) )
?>
<li><a href="<?php bp_members_directory_permalink(); ?>"><?php printf( __( 'All Members', 'buddypress' ) ); ?></a></li>
<li><a href="http://buddypress.org" target="_blank" title="BP">BuddyPress</a></li>
<?php  
}
add_action( 'bp_member_options_nav', 'bpfr_custom_setup_nav' );

Try this:

// depending the theme Main Menu, somwhere near Home, About, etc
function bpfr_custom_setup_nav( $items) {
	
    if ( is_user_logged_in() ) {		
        $items = '<li><a href="'. bp_get_loggedin_user_link() .'activity/news-feed/">News feed</a></li>';	
    }
    return $items;
}
// 10 is the priority, 1 is the position in the menu
add_filter( 'wp_nav_menu_items', 'bpfr_custom_setup_nav', 10, 1 );

 

References:

wp_nav_menu_items

https://codex.wordpress.org/Function_Reference/wp_get_nav_menu_items