The term 'Flying Nuisance' can be broken down into two crossword solutions: GNAT (4 letters) and DELAY (5 letters). A GNAT is a small, flying insect that can be a nuisance due to its buzzing sound and the fact that it often swarms around people. Gnats are also known to bite humans and animals, causing irritation and discomfort. A DELAY is an interruption or postponement of an event or action. In the context of a flying nuisance, a DELAY could refer to a disruption in travel plans caused by the presence of gnats.