In Florida, two private citizens can sell/buy said lawful firearm.
You may not transfer NFA w/o proper steps being taken.
As an aside, if you sell to a person, and they're a b/g, the LEOs may come looking for you if your gun can be traced to you. So, to avoid a b/g, ask to see their concealed carry license. If they don't have one, ask why? Just be careful who you sell to and you should be okay.
If you buy from somebody, same thing applies - if they have a concealed license, then they are probably an okay person and not selling a stolen firearm. Etc., etc., etc.
What are you selling/buying?
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"I'm no big city lawyer, but..." as far as the shipping goes - DO NOT ship via USPS!!! I'm not sure about UPS, but I don't think a non FFL/C&R can ship to another non FFL/C&R person - I think you need to go through an FFL/C&R to ship. That being said, I don't know if FedEx, or another type of courier, has the same thing apply. Moreover, if you were to ship to the other person and not inform anybody what is in the box, you might get away with it, then again... you might not. I believe in face-to-face for firearms transactions.
Just my $.02