Flowing Stream City was about a two day journey away from the Heaven Supression City. But Rein and his group were going to use a great beast to pull their carriage, so it was not going to take that long for them. This great beast was tamed by the sect which most of the time was only possible if that beast was already tamed before awakening as a great beast.
So with that beast pulling their carriage, it took Rein's group only about 10 hours to reach the city. It was still a long journey but 10 hours was a great improvement if compared to the 36-40 hours that it would have normally taken.
