The answer to 'drain cleaning won't flush' is that a clogged drain is the most common cause. This can be due to a buildup of hair, soap scum, food debris, or other materials in the drain pipe. Symptoms may include slow draining water, gurgling sounds, or a foul odor coming from the drain.
To fix a clogged drain, you can try using a plunger or a drain snake/auger to dislodge the blockage. If those DIY methods don't work, it's best to call a professional plumber who can use specialized tools and techniques to thoroughly clean the drain. They can also identify and address any underlying issues causing the clog.