There are no accredited vet assistant programs. Sorry. The American Veterinary Medical Association (AVMA) does not recognize veterinary assistant programs and does not accredit them. You do not need any formal education to be a vet assistant. On the job training is preferable. Realistically speaking this is not a career. As veterinary clinics are getting larger and lawsuits against veterinarians are becoming more plentiful more and more clinics are hiring registered technicians instead of assistants. The term assistant has come to mean the high school kid who feeds and walks the dog or the person in the front office who answers the phone. No education is required for these positions.
If you truly want a lifelong career in a vet clinic consider a vet tech program instead. They do take longer (2 years) and award an associate's degree. But, you will be getting something for your education and the job opportunities are much better. There are a few on-line programs and most accept federal aid. Here is a list of on-line tech programs that are AVMA accredited.
I know I didn't really answer your question but what you are looking for simply doesn't exist.
Vets really don't have a clue about cat breeds. They only know which diseases certain breeds are prone to and write down whatever YOU tell them your cat is. Breed recognition are breed standards are not part of medical school.
Why'd you take her if you can't afford vet bills? Did you get her spayed, up to date on shots, deflead, dewormed, tested for disease and microchipped? All of that is going to cost you around $300-$400.
Your kitten is only a breed if your friend bought it from a breeder and has papers to prove its breed. Highly unlikely she'd spend the minimum $600 to buy a pedigreed kitten and then just give it away. Your kitten is simply a "domestic" - a kitten of no particular breed just like over 97% of the cats on this entire planet.
edit: if you mean the kitten picture on your Yahoo Pulse profile it's a Black Tortie and White domestic - a kitten of no breed. It looks VERY young. How young is it? It should have stayed with the mother cat until it was at least eight weeks old. This kitten can't be more than five or six weeks.
edit2: LOL at your comments. And yes - it'd be pretty stupid to take a cat to a vet to find out their breed because most vets don't have a clue - nor are there any tests to determine cat breeds. And LOL that you thanked "Christina" for her answer. Calico isn't a breed. It's a coat pattern. And actually your cat has far too much black to be Calico - it's Tortie and White. And again - your cat isn't any breed.