BuddyPress.org

bp_core_get_user_domain( $user_id ) will output something like http://example.com/members/andy/

Note:

1. You will need to get $user_id before hand. How you get that will depend on the page you’re viewing on the site. This article will explain more:

Playing with the user’s ID in different contexts

2. To append ‘activity’ to the URL, you can use a period .

For example bp_core_get_user_domain( $user_id ) . 'activity' will output something like http://example.com/members/andy/activity

3. To wrap that URL in mark up

<a href="<?php echo esc_url( bp_core_get_user_domain( $user_id ) ); ?>"><?php esc_html_e( 'Text', 'text-domain' ); ?></a>

You can add such a link very simply to your main menu by using the menu customizer:
http://example.com/members/me/

Read: https://buddypress.org/support/topic/dynamic-profil-link/#post-259834

Good shout @danbp 🙂