Yes if you are going into business to clean other peoples weapons and if they leave them with you. You will be required to obtain an FFL License. Then you will need to acquire insurance which is very difficult if you are not a certified trained gunsmith. Most insurance companies will not issue a policy. The other issue is personal liability when working and disassembling of customer weapons. Best to have an LLC Corp which does help to protect your personal property. It is not the total answer but recommended by most legal advisers. So it is not just as easy as starting to work on the weapons free lance! This is not to discourage you only to give you some guidelines regarding doing business with weapons. The weapons would also be entered in your FFL Book if they left the weapon with you and signed back out when they picked it up later.
Good luck and I encourage you with your goal of going to a certified gunsmithing school.
The other option is you can get in with a local gun dealer and operate under his or her license at their location making some extra money doing the same thing. You would technically be their employee when working on weapons at their facility. I have a friend that does that with a local dealer to make extra money. He gets no hourly wage from the shop but makes his money cleaning and repairing as a service to the shop? Everyone gains in this situation if there is enough business. Also you could advertise for the shop and your repair service. Only an idea! But even then I would be sure his insurance covers you and your work.
The Constitution is not an instrument for the Government to restrain the people. It is an instrument for the people to restrain the Government!
“Americans have the right and advantage of being armed. Unlike the people of other countries, whose leaders are afraid to trust them with arms.”
James Madison. Author of the 2nd Amendment