free cna courses in Los Angeles, CA?

try your local community college. the program where I am taking made all of us apply for the grant they had and if you qualify you they will get you covered. goodluck

Try your local "Works" department (if you have one and I think most states do), A.K.A unemployment agency. They may be able to tell you how to get that training.
In some states, some nursing homes will give you the training IF you commit to working for them for a year.

I personally borrowed money from family to pay for class at the Red Cross and my state reimbursed me for most of it once I passed the state test and began working in LTC.