Aircraft is a very general term which covers many various kinds of machines that can fly - including helicopters, military aircraft, gliders and so on. An airplane is a specific type of aircraft - it has an engine and fixed wings. Note that 'airplane' is the North American term - elsewhere, English speakers use 'aeroplane'. 'Plane' is simply a short form of both 'airplane' and 'aeroplane'. 'Flight' is the noun derived from the verb 'fly'. A flight is not an object - it's the action of flying. If you say 'What time is your flight?' or 'I took a flight to Paris', you are referring to the service which the airline provides.

An airplane (aeroplane) is a type of aircraft. Helicopters and blimps are also aircraft. Plane is a shortened way of saying airplane but it can also mean a flat expanse of material or space in math. As a verb, it can mean to make a board smooth, flat and uniform in thickness. Flight is a noun for what an aircraft accomplishes. For example, many airplanes make flights between Los Angeles and San Francisco.