For a private sale you file the exact same paperwork as if you were buying it from a dealer, and you have to wait for the transfer to be approved before you can take possession of the item.
So you pay the individual for the suppressor, file all the paperwork and submit your transfer fee, wait for the ATF to approve the transfer, the ATF sends the approved form back to the seller, then the seller lets you know that you can come and pick up the suppressor.
This only works if the seller and buyer are both residents of the same state. If they are in different states, the seller has to transfer the suppressor to a FFL/SOT in the buyer’s state (tax paid transfer), and then you would start the transfer from the FFL/SOT to the buyer (tax paid) as normal. That means double the taxes and double the wait, which means it’s not really feasible unless we’re talking machine guns.
I hope you’re getting a good deal on the can. Most used cans I’ve seen are sold at a significant discount compared to the new price.
Also, I recommend only doing a private sale with someone you already know and trust. This person will have both your money and the suppressor for somewhere between 6 months and a year (depending on the ATF) and you are trusting them to be prompt when they contact you to pick up your can once the ATF sends them the transfer approval.
That doesn’t get into the issue of the seller using the can after you’ve paid for it but before the transfer comes back. It would suck for the seller to have a baffle strike while you’re waiting for the ATF to approve the transfer.
