RE: how do you transport a kit on a airline
Assuming you will be taking the ARF before assembly, it is unlikely that you will be able to take an ARF box onbard... You should be able to send it as checked baggage, possibly at some extra charge, and if it is boxed within a box with additional packaging, appropriately and prominently marked, it should arrive OK.
The other thing you could do is package it appropriately send it to yourself via Fedex or UPS... Would be less hassle (schlepping an ARF box plus your baggage thru the airport is gonna present some interesting moments.) and may not be any more expensive, depending on the airline's policy for oversized baggage...
HTH
Jim