Anti-clogging chemical solutions can be used to remove a blockage from a kitchen sink that is clogged, even if both sides of the sink are clogged. Begin by first removing all dishes and drain plugs from the sink. Pour the chemical solution slowly into the clogged drain or drains. Then allow the chemicals to sit in the drain according to the package directions, usually for about 10 to 15 minutes. Then use hot water to flush the drain, allowing the water to run for several minutes. If the water still does not drain freely, then repeat the process. Clean the sink thoroughly to remove any leftover chemical residue before resuming normal use of the sink. If the clog remains, a metal "snake" may need to be used to forcefully remove the blockage. Such items can be rented, and plumbers use them as well.