Air Genasi in 5e D&D have the trait Unending Breath. Does this trait carry over when an Air Genasi druid uses Wild Shape? Would such a druid be able to breathe on land if they wild shaped into a fish or other strictly water-breathing animal?
The description of Wild Shape states:
You retain the benefit of any features from your class, race, or other source and can use them if the new form is physically capable of doing so. However, you can't use any of your special senses, such as darkvision, unless your new form also has that sense.
Presumably any beast you can wild shape into would also be able to hold its breath, in which case you would indeed retain the benefit of the Unending Breath racial feature.
It would not let you breathe where you would otherwise be unable to, or change anything about flight. The feature does exactly what it says it does; it lets you hold your breath indefinitely while not incapacitated. (Normally, a creature can hold its breath for a number of minutes equal to 1 + its Constitution modifier (minimum of 30 seconds).)