Yes, there is such a thing as professional knappers. Most are retired but there are some younger guys who are making a living at it. Of course, it helps to diversify into other areas like making/selling flintknapping tools and collecting/selling flint, for example.
Some knappers can make $1000+ for a single piece but these are usually very large pieces and/or made from exotic materials that are expensive to begin with. But you can probably count these guys on one hand. It's a very specialized niche.
There are also people making fakes and selling them for good money on the black market or to uneducated buyers. I won't get into this aspect other than to say that professional counterfeiters have been around from the very beginnings of modern flintknapping. At least since the 40's or 50's.
Some professional knappers can be found making "the rounds" at knap-ins across the country. I've met a couple but I haven't asked what they average per month. It can't be that much. I think most of the money to be made is through online stores. From what I've seen in sales, I would guess that $3000 per month is on the high end.
As for me, I could be knapping full time and selling everything I make but the hourly rate would be something like $10 at best. You gotta remember there's a lot of expense in getting good stone, lots of breakages, shipping time/labor, store maintenance, email time, and tool costs. I could make more than $10 per hour if I concentrated on large, thin, translucent reproductions of real artifacts but some of these would probably pass thorough several hands and eventually end up in collections as "real". That thought really bugs me and makes me sick to my stomach. So I tend to back off from reproductions... and the "big" money.
If I had to describe making a living as a knapper in simple terms, I would say it's a lot like trying to make a living at gambling. There's a lot of specialized knowledge needed, a lot of competition for the money, and a lot of temptation/opportunity to go to the dark side.