As a National Master offering private chess lessons to individuals in the United States, what are the normal hourly rates?
It seems that a good answer to your question is that the fee depends on the instructor.
In my perspective, fees for chess lessons are between $0 and $500 per hour. Instructors who charge $0 are volunteers who love to do something good for humankind and do NOT need the money. Instructors who charge $500 are teachers in high demand, have a big number of customers, and have access to very rich people.
Some instructors charge $5 because they live in countries with low living costs. Moreover, they are from non-English speaking countries. Additionally, if they charge $5 per hour because they do not have too many customers. A more common fee for online instructors from non-English speaking countries is $15-25.
Instructors who live in the United States usually charge $50-100 per hour. This has a lot of sense because in some areas of the United States if you work in the fast-food industry, you start with $17 per hour. A good guess is that to make a living in the USA as a chess instructor, you need to charge $100 per hour and have enough customers who have the financial resources, and the willingness to consider lessons from that instructor a good investment. Only people with an excellent income can afford to pay $100 per hour. That is the reason why books and videos are so popular as an alternative, or as a complement, to chess tutoring that is expensive.
Lichess.org and chess.com have a section for instructors. You can find several names there. Also, if you are looking for someone in your area, look into craiglist.org. In addition to that, there are many websites that offer teaching services, just Google it.
Something interesting is that a national master and even a instructor without a chess title can charge the same or more than a grand master. The logic behind this is that a grand master will play better but not necessarily will be a better instructor. One excellent example is Steve Giddins, who is not a grandmaster, but he is a formidable writer and lecturer. One of his former students is grandmaster Matthew Sadler. Steve Giddins is a FIDE master.
Good luck in your chess journey!