Если в запросе также разрешен выбор столбца date_created, мы можем заказать объединение результатов как -
(SELECT A.user_id, A.friend_id, B.username, B.avatar, A.date_created as createdDate
FROM users_friends AS A
INNER JOIN users AS B
ON A.friend_id = B.user_id
AND A.user_id = 3
AND A.friendship_status = 1)
UNION
(SELECT A.friend_id, A.user_id, B.username, B.avatar, A.date_created as createdDate
FROM users_friends AS A
INNER JOIN users AS B
ON B.user_id = A.user_id
AND A.friend_id = 3
AND A.friendship_status = 1)
order by createdDate LIMIT 10