Flying with boxed models

you may want to look in to shipping them. depending on luggage space it may be cheaper.

Shouldn't be a security problem, maybe a baggage problem (box size vs. luggage allowance),

but I've put kits in my case hold luggage (well wrapped in shirts, etc) without problems.

I'd avoid paint & glue in case some jobs worth quotes 'health & safety' & gets the rubber gloves out! 

As long as its only the models, I see no problem. I have done it, but this was many, many years ago, and I was only flying from England to N Ireland. But I see no problem as its only plastic.