You can use wp_nav_menu_items
filter for this, and check if user logged in, and use get_author_posts_url($autho_id)
as bravokeyl suggested:
add_filter('wp_nav_menu_items', function( $items, $args ) {
$index = 'top-menu'; // menu index key, if you're not sure then var_dump( $args->theme_location )
global $current_user;
if ( $current_user->ID && $index === $args->theme_location ) {
$items .= sprintf(
'<li id="menu-item-my-posts" class="menu-item menu-item-type-custom menu-item-object-custom menu-item-my-posts menu-item-my-posts"><a href="https://wordpress.stackexchange.com/questions/247427/%s">%s</a></li>',
get_author_posts_url( $current_user->ID ),
'My Posts'
);
}
return $items;
}, 10, 2);
Hope that helps.