Isn't it supposed to be shu fly. you know like the old saying shu fly don't bother me. So in the song it would be shu fly dragon fly, get back to mother. If you're from the country you can understand why he would shu the dragon fly away, especially if you're swimming.
the log is like a favorite old fishing hole. Catfish are usually found "laying" near old logs for a food source. So a good spot to fish for big cat's is by "the old log".
hope that helps.