Hi Graeme,
Welcome to Buddydev forums 🙂

Are you using BuddyPress clear notification plugin? If yes, you can create a function like this and use it anywhere

function buddydev_clear_notification_button() {
	
	if ( !  is_user_logged_in() ) {
		return ;
		
	}
	
	$user_id = bp_loggedin_user_id();
	
	$notifications = bp_notifications_get_notifications_for_user( $user_id );
	
	if ( ! $notifications ) {
		return ;
	}
			
			
	echo '<a id="clear-notifications" href="'.bp_core_get_user_domain( $user_id ).'?clear-all=true&_wpnonce=' . wp_create_nonce('clear-all-notifications-for-'. $user_id ).'"> [x] Clear All Notifications</a>';

}

Here is an example to show how to inject it at the top in the notifications screen(It is not the right way, the notification template does not have a hook, so I suggest using the function in the template directly instead of hooking like below)

function buddydev_inject_clear_button() {
	
	if( !  bp_is_notifications_component() ) {
		return ;
	}
	
	 buddydev_clear_notification_button();
}
add_action( 'bp_before_member_body', 'buddydev_inject_clear_button' );

Hope that helps.
Please do let me know how it goes?

Regards
Brajesh