Hey, I fell down an internet blackhole and somehow ended up at a blog that mentioned the idea of CANZUK which I'd never heard of before. I googled the term and read this thread. I just completed a drive from Texas to Virginia and had too much time to think. I don't know if anybody is going to read this, but . . .
Obviously this union has about a 0.0000001% chance of happening, but here's a proposal that would have the best chance of passing.
1. Free trade, obviously. Constituent countries retain the ability to set trade parameters with other nations outside the federation.
2. Free movement of native born citizens between each constituent country. Each country can set it's own policies regarding immigration from outside the federation and immigration of naturalized citizens from other constituent countries.
3. Combined naval / marine corps command. Each country makes a binding commitment to fund a combined navy at a certain % of GDP. This navy can be used at the request of any constituent country subject to a veto in which all three other countries unanimously oppose action. Each nation can keep a small independent navy if wanted. The breakdown could be something like 3/4ths of total current naval spending of constituent nations goes to the federation navy while 1/4th is used to build independent navies. Each government would appoint civilian naval secretaries to oversee the force. The structure would be something like a more unified NATO.
4. Each country retains separate armies and air forces, but technology and training is standardized for easy combined or independent use. Create a permanent skeleton federation command structure so integration can be quick in the event of a combined declaration of war from all constituent countries.
5. The flag . . .
This is the current British Naval flag
Fill in the upper right and lower left corners of the flag with a blue background. Place the red southern cross (for NZ's flag) and the white southern cross (from Australia's flag) in those quadrants. Put the red maple leave in the lower right quadrant. This can be on a blue background or on the current white background as with the Canadian flag. This would be the naval flag and could be hung at a level below the national flag and the regional flags (Scotland, Alberta, ets) throughout the federation. This would emphasize that the constituent countries are the top level of authority and prevent federal creep.