why does baking soda and vinegar unclog the drain?

I agree with Tangle, bicarbonate is not a strong enough base to react with fats (it will react with free fatty acids, but not intact triglycerides), so it is probably not doing anything to any grease if that is what is slowing the drain. The unclogging action is just the release of CO₂ causing expansion and agitation.A clogged vent usually doesn't cause a drain to run slow, it usually causes gurgling like you would get if you tried to pour water from a jug too fast. So don't risk your life going up on the roof just yet .My guess is that the clog is beyond the reach of your snake. A couple suggestions1) If you have a clean-out fitting between the kitchen sink and where you know the drains to be clear, try running the snake from there.2) Use a commercial drain cleaner. Allow the pipes to sit long enough to allow the water to run out of the system (overnight maybe) and pour in the recommended amount of drain cleaner and run enough hot water to get the drain cleaner to the clog. You may need to repeat this once or twice.3) Use a plunger on the sink drain, working it in and out to try and dislodge the clog. Of course, be very careful if there is any drain cleaner in pipes.If this does't work, you probably should call a plumber.Once it is unclogged, I would recommend a couple things. First, if you have a garbage disposal, try to minimize the amount of food you put down the drain. Compost instead. Those food particles can get stuck in the drain and cause build up - much like what happens in your arteries. Second, use an enzymatic cleaner a couple times a year. These products use enzymes and/or microbes that break down greasy sludge build up in your pipes and helps keep them clean.Hope this helps, I've been there before. My wife used to go crazy with the garbage disposal, putting EVERYTHING down it. She would clog it every 6 months or so. The last time it took 3 days to unclog it, using the methods above.HBD