How do I get water in my kitchen sink to drain?

Hi I'm PeterHow long did you wait between the three bottles of cleaner. Some say wait 15-30 minutes then flush with hot water. It sounds Like your problem is further down the line maybe at the elbow where the vent pipe and the T connector is. I have gone on the roof and ran a drain snake down through it and unclogged the drain. Another method which I normally do not recommend because it can be very dangerous if you have already put caustic drain cleaner in the system. I have taken my air compressor and put an open tip on the hose while the line was crimped then stuck the end as far as I could in the pipe then wrapped a towel around the drain to seal it then release the crimp on the line shooting 120 PSI into it. This will blow a clog out a lot of times however you will need safety glasses, gloves , face shield and whatever else if you were crazy enough to do it after you put the caustic cleaner down it. The air pressure can back blow what ever liquid that is in the pipe back in your face if there is not a good shield. I repeat EXTREMELY Dangerous. I do it but I handle these type of situations all the time. So be warned. My preference for treatment before anything is a gallon of bleach let it sit for 30-60 min. then flush as hot as water as I can down the drain. Most of the time I never have to do anything else. Be careful you don't slip if you go on the roof to access the vent pipe
Good luck.

Remove drain pipe under sink with u shape clogged easy but use gloves due to drain cleaner. Drain cleaner only works on hair