Is it permissible for one afflicted with urinary incontinence to perform ablution immediately after leaving the restroom and wipe over his socks, while urine continues to flow during ablution, in order to catch the prayer or work, or is it a condition to wait for the incontinence to stop, knowing that he is excused?

If a person's urination stops after a period, and they are able to purify themselves and pray without any urine coming out, then they are not afflicted with urinary incontinence ( سلس البول). They must wait until the event (urination) ceases, then perform ablution (وضوء) and pray. They should relieve themselves with sufficient time to be able to perform ablution and catch the prayer, because they are not among those for whom concessions are made, like the person with incontinence or a woman experiencing post-partum bleeding (مستحاضة).