Since 2nd grade I always wanted a Cham, but we were always moving around the world. Right after the most recent move, I seized the opportunity and spent months getting supplies, researching, and getting ready for my very own Chameleon. I finally got Vincent and I've had him for about a month. There is a possibility that my parents work will take us to another country within the next 5 years, and It would break my heart to give Vincent away. In the future would it be possible for Vincent to go on an airplane with me? Or is there possibly another way to safely transport a Chameleon over the ocean?
The short answer is that it will prohibitively expensive and very difficult to do. Also, at 5 years of age, the animal will be quite old. The costs are a lot more than just the transport costs.
Where are you located now? A lot will depend on where you are and where you will relocate to. What species is it? Where did you buy it? Is it captive bred or wild caught? If captive bred, do you have documentation to prove that? If wild caught, you will need the original CITES permits for when it was imported into the country you are in now.
If you are in the US, you will need a ton of paperwork and it is not cheap. Other countries will require most of the same paperwork, but they often do not charge for it. US Fish and Wildlife is a nightmare to deal with. If you are in the US, they are the people to start with.
As far as I know, all chameleons are governed by CITES, which is the Convention on International Trade in Endangered Species. There is a huge difference in how animals and animal parts move across borders depending on whether they are CITES Appendix I or CITES Appendix II. A HUGE difference. CITES I animals are things like rhinoceroses and their parts, elephant ivory--highly endangered and heavily regulated animals. If CITES I, you will need not only a CITES Export permit, but a CITES Import permit for the country you are going to. Permits are issued for only a certain amount of time and everything has to be coordinated.
Last year, I needed several affidavits for a CITES I import. More $$$$. Lots more $$$$$.
First you need to find out if your animal is CITES I or CITES II.
Next, you will need to find out if the importing country has requirements for importing the species you have. I believe places like Australia simply do not allow the import of any chameleons.
Once you know where you are going and when, you need to know which airport you are flying out of. US Fish and Wildlife will need to inspect the shipment (and stamp the CITES Export papers) and they will charge you about $250 fee for that. Other countries might simply stamp the paperwork and not charge you (Canada for example). You must have the export paperwork stamped, etc., by the exporting government agency or your don't have the proper documents to import the animal into the new country.
There are only a few official ports that you can go through into or out of the US. If you fly out of a different city, you might need a Port Exemption Certificate (more $$$$$). You have to make an appointment for inspection of your shipment. The Department of Agriculture might also need to inspect the shipment, but I doubt it for outgoing shipments. Again, if they do, more $$$$$.
That's just the paperwork and is probably not even everything you need.
Last, you can worry about shipping your animal, which was the original question you had. Yes, they cope very well if packed properly, but again, more $$$$$.
Bottom line--find him a new home!