If flushing doesn't work, you need to physically break the blockage.
If your fridge drain keeps freezing over, this is a technician trick: how to clear blocked fridge drain
Once you believe the clog is clear, pour a small amount of water into the hole. It should flow freely and disappear quickly. You can check the drain pan underneath the fridge (remove the kick plate at the bottom front of the fridge) to see if the water has collected there. If flushing doesn't work, you need to physically
If you have cleared the drain and water is still appearing: If flushing doesn't work