A flop house is an old term for a temporary boarding house, where tenants stay to sleep (flop) for short periods of time.
Electric tooth brushes were still a novel product at the time of this short. Because they were operated by plugging a cord into a power outlet, some felt they were possibly unsafe as well.
The whole short is a play on the concept of a drunken person hallucinating and seeing pink elephants. This was shown in the Disney film "Dumbo" in 1941.
The interaction between the drunk and his (presumed) sponsor is a fairly accurate (if humorous) portrayal of how AA and similar organizations work to combat addiction one on one.