I think my kitchen drains are partially clogged because the sink drains slowly. What do you recommend?

First, try using a plunger. Try using a liquid drain opener if that doesn’t work, but use caution and read the directions. Remove the trap and any debris. Be careful if you have used a liquid drain opener because there may be some in the trap. However, if the clog is beyond the trap, there are drain augers that extend from about 15 feet to about 50 feet. There are also special enzyme-based drain openers, that will help dissolve buildup in pipes in older homes.