What is the ruling on the prayer of someone who suffers from intermittent urinary incontinence, where urine sometimes exits during movement while performing ablution?

You must have a good opinion of Allah and remember that He has not placed any hardship in religion. It appears from the question that you are afflicted with waswasah (whispers/obsessive thoughts). Therefore, turn away from these waswasah and do not pay attention to them. Do not rule that something has exited unless you have absolute certainty, as the default is that nothing has exited when in doubt. Perform istinja' (cleaning after relieving oneself) after answering the call of nature and ignore the doubts. If you are certain that urine drops are exiting after urinating, place a cloth or a paper towel until the discharge stops, then perform istinja' and wudu' (ablution). If the urine discharge is continuous and does not stop until the time of prayer exits, then perform wudu' after the prayer time begins, and whatever exits will not harm you. We ask Allah to cure you from waswasah and we advise you to supplicate and consult a trusted psychiatrist.