I have this really nasty black spot where my N used to be, where the original color of my bumper is coming through. (blackness).

Is it possible to 'patch' this by wet sanding, and then repainting it only there in like a square and air brushing the edges?

If yes, who can do it and how much? I have some of the original car paint...

 

Depends on how good you want it to look. There are skilled painters that can do what you want, but it likely won't look great and more than likely will get worse with age.

First question is, why did it flake off to begin with? If it's peeling all over due to adhesion problems, save your money and get the whole cover re-done.

If it's a problem caused by some impact or other issue that damaged the paint, then a repair is a good way to go.

If you're going to pay someone to do it, do it right. Prep, paint, blend the color, and clear the whole bumper cover. $200-$250.