How is it possible to get bladder cancer, since your bladder always flushes itself clean?

Toxins: Although the bladder is always "flushing itself", it still holds urine for an extended period of time when you hold your urine for several hours between voids. It is felt that during this period of time, the carcinogens exposed to bladder can promote cellular damage and eventually lead to bladder cancer since they are in continuous contact wit the bladder lining.

Long term exposure: Your point is well made. Most cancers of the urothelium occur on the "floor" of the bladder where urine contact is most prolonged. The upper urinary tract (renal pelvis and ureters) are less frequently affected despite similar exposures. Toxins in the urine (eg, from cigarette smoke) induce changes over time which can lead to cancer formation.