There's an accumulation of black slude in my bathroom sink drain and it's preventing the water from draining properly - - it's just getting worse and I'm wondering what to flush down the sink to get rid of it.

Some draino would do the trick
You can get it anywhere

I don't know what causes the formation of the sludge. Periodically I notice that a bathroom sink is draining too slowly. When water covers the sink drain, the water will drain slowly for awhile and then will burble. After that, the water will drain So I put a small bucket under the trap and remove the trap and stopper.

The trap is always nearly perfectly clear. Typically I find only a bit of gooey black goop on the upper surface of the trap. However, the stopper is coated with gooey black sludge and the tailpiece pipe is clogged with gooey, goopy black sludge. The tailpiece has a series of holes arranged around its circumference. These connect to the overflow and have two functions. They prevent water from overflowing and they act as a drain vent. Usually the black sludge is restricting airflow, preventing the sink drain from venting and causing a slow drain. I clean the vent holes out with a screwdriver. Then I ball up a sheet of paper towel and force it through the open tailpiece pipe . Typically a big blob of gooey black sludge falls into the bucket. I repeat until I have cleaned out the obstruction, The sink then drains well.

I wish I knew the cause of the sludge and could prevent its formation.