Is it obligatory for a person afflicted with urinary incontinence to walk a long distance until it stops, or is he considered afflicted with incontinence and takes its ruling, given the hardship involved?

If the emission of urine is irregular, then the ruling of incontinence ( سلس ) applies to you. In this case, you should perform ablution (wudu') for each prayer after its time has begun, and then you may perform as many supererogatory (nafl) prayers as you wish with that ablution. There is no requirement to undergo difficult treatments for incontinence.