Sorry to burst your bubble, but working in a restaurant kitchen for no pay is illegal and it's the restaurant owner/manager/chef's responsibility to know that. Trailing for a night is one thing, but having a regular part-time schedule as you have described sets him (and you) up for huge liability issues with several different governmental departments.
If, for example, you were hurt on the job, or harrassed, you would have no legal protection or access to compensation for your injuries if you are not on the payroll. This could set him(the owner) up for significant fines and lawsuits. In another scenario, if you were inadvertantly responsible for damaging some part of the operation (breaking an expensive piece of equipment, starting a fire, etc.) those damages would not be covered by his general liability insurance since you were not an official employee; then you could, concievably, be held personally responsible for those damages.
It's easy to think that you employer is doing you a favor and he would not be an SOB under such circumstances, but most restaurants walk a narrow line financially, and a major liability case tends to bring out the worst in people.
The chef is not legally able to make people work for free-even if they are low-skilled. That's what internships and training programs are for. Insist that he pay you minimum wage if you feel that you want to continue, or at the very least, have someone craft an unpaid internship contract for both of you to sign with copies for each. The contract should stipulate a specific time period for the intership, work duties and employee/employer protections.
You may not have a lot of confidence in the value of you skills, but believe me, you are providing that chef a considerable service by cutting up potatoes or onions, or eve just cleaning out the coolers.
Remember, indentured servitude has been illegal in this country for many, many years. Somehow, the food service industry skirts the law quite frequently, but when individuals are caught at it, the penalties are severe.