Layered sheet metal is not a very cheap, or easy way to make a
sprocket. Or much of anything. They use the technique to make
transformers, but for totally different reasons.
I would be slicing the final thickness you want off of round bar, with
a small 4x6 horizontal bandsaw- its gonna be cheaper and quicker in the
long run, and the bandsaw is good for a million other things.
Yes, you could cut circles in 16ga with a flycutter- but to do it in
much quantity, you would probably want a milling machine, with a collet
system that actually locks in place with a drawbar- nothing quite as
exciting as when you flycutter overpowers the friction fit of your
morse taper drill chuck, and decides to go for a spin around the shop.
2" circles are usually stamped on a punch press.
And you can buy em cheaply from companies that do this by the thousand.
The tonnage required to punch a 2" circle from 16 ga is more than you
would think- probably around 12 tons. Can you hit a hammer that hard?