I'd say 18 gauge plates.
Each about...hmm....2 inches across?
They need not all be the same size for every part of the jack,though.
Smaller plates for tighter areas like armpits, or neck ring maybe.
The plates assembled in this manner will all overlap about 50%, so you can use thinner than what you'd want in say, a coat of plates.
I'd add a little extra to the edges of the cloth when you pattern the jack shell.
Just enough to account for the extra layer or plates, and maybe padding if you stuff padding into it instead of using a separate padded layer under.
You can always trim the edges down later when you finish the garment.. But, say, an extra half inch gives a little more forgiveness for the plate layer and the expansion it creates.
The pics I have seen of original jacks look like they have a half inch or so of stuffed padding under the plate layer.. I could be misreading the images, but I don't think so.
The edges where I can see them are quite thick, and a padding layer would account for that.
From what I have read, plates were made from just about any old iron scraps or old plate armor, cut into squares, painted and punched with a hole of around a quarter inch through the middle.
(For the cording to have enough clearance to pass through three times, the hole has to be reasonably generous- 3/16 to 1/4 inch seems about right to me.)
For the record, a jack of plate has been on my to-do list for a couple of years....
So I have devoted some time to thinking about the details.

It also occurs to me, that the thin version of 2 inch fender washers could be used to make a jack, if round plates are in consideration. (Around here, 2 inch, 18 or 20 gauge fender washers are carried by Lowes.)
They would be galvanized and with a convenient hole in place already....And easily obtained in numbers.
If they would lay better curved- they could just be dished lightly with a wooden block and a hammer or leather mallet.
Just my two cents worth.
-Badger-