Interesting question. First I had to blow the dust off my forty year old degree in materials science, but even that was not a lot of help since they did not teach us much about wood. There are two issues to be looked at in order to answer Peter's question about the metal lined head joint.
First question is whether the drying-induced shrinking of the wood creates enough force to compress the liner tube appreciably. If it does, then the reduction in diameter of the liner tube will relieve the stress on the wood and make it less likely to crack, particularly for thicker sections of wood. To answer that question you need to know the elastic modulus of the materials. Information is hard to find, but with a few assumptions and the information in
http://www.fpl.fs.fed.us/documnts/fplgt ... 3/ch04.pdf it looks like the modulus for a tropical hardwood, in the radial and tangential directions should be around 100,000 to 200,000 pounds per square inch. The modulus for silver is around 10 million pounds per square inch, so silver is 50 to 100 times stiffer than wood. In a typical head joint the wood is about 10 times thicker than the metal, but even with that difference the silver would not compress very much at all. If that is the case and you can treat the silver as incompressible, then the thickness of the wood should not make much difference to whether it cracks or not.
The other question concerns how the wood dries out, and the moisture gradient in the wood. As Paddler observed, thicker pieces of wood are more likely to crack as they dry. This is because the outside dries and shrinks while the inside remains moist (and therefore not shrunken) for much longer. This sets up stresses in the piece of wood, with a tensile stress at the outer surface which causes the cracks. The thicker the wood, the higher the stress, which is why flutemakers like to pre-drill and rough turn their wood as soon as possible. This effect could contribute to cracking of a lined head joint, especially if it was improperly seasoned or stored in a very dry place, which underlines the points Loren makes.
I don't pretend that any of the above is a rigorous analysis, though it would be great if someone with time on their hands could do some real calculations. I think that in the end I would have to agree with Loren that the most important things are getting a flute made from well seasoned wood and taking proper care of it.