Do you need to flush a toilet periodically to keep the wax ring from drying out

No. In fact, in a properly functioning toilet, the wax ring doesn't get wet. The wax ring seals sewer gasses from escaping since the ring is below the water trap. If the toilet backs up, it should keep the waste water from leaking out onto the floor.

This is the theme of a Seinfeld episode. Jerry has to go away and he asks George to periodically flush his toilet to keep the 'seal' from drying out.

Wax rings are not real wax. They stay flexible and won't dry out.

That would be kind of like saying we need to put water on our candles from time to time to keep them from drying out.

Maybe Joy should tell us if George actually flushed Jerry's toilet while he was gone, and did it help. I missed that episode.

LOL. I think George and Kramer got into a fight over who was asked to do it.