The resistance of aluminum to burning is generally proportional to its thickness. What happens is, the outer layer, if thick enough, conducts heat away from a hot spot to keep a concentrated heat source from burning through. Stove design has a lot to do with whether you can get away with aluminum. Off hand, I can't think of a wood stove design that will not have hot spots. I have burned up several in attempts to use aluminum flashing. If you use aluminum sheet heavier than flashing, not only is it hard to work with, but after a certain point, you might as well use steel.
Before you knock yourself out making a fancy wood-burning stove, consider a couple of things. First, can you use it where you camp? Many state and national parks prohibit any gathering of any plant material - that means fire wood - even blow-downs and forest litter. Second, if you can legally use a wood stove, you might try it out on a short trip or two. You may decide you don't like the smoke and sooty mess.
If you decide to experiment with a simple, inexpensive, easy-to-make and effective wood stove to see if you like it, my favorite is very simple: a 28 ounce tomato can with holes punched around the bottom with a church key and enlarged a little, and a triangle of three interlocking 1/16 aluminum bars made from 1.5 inch X 1/16 inch bar stock as a pot support. Home Depot, Lowe's and most other hardware stores have this stuff at about $5 for 3 or 4 feet. If you want to get fancy, a support screen, 1/2 inch off the bottom, made of stainless hardware cloth might improve ventillation a little, but it is probably not worth the trouble. This rig fits in a half liter pot and weighs 5 ounces.
If you want an even easier construction job to see if a wood stove is for you, make the pot support by cutting 1.5 inches off another can and squashing it into a triangle that will sit on top of the burning can. Notch the bottom to fit the rim of the can to make it sit securely. Making this rig will take a grand total of 10 minutes, at the most. It might not pack as neatly as the interlocking aluminum bars, but it will do for a try-out.