There are certain disqualifiers for military service, but I'm not sure if Autism, or certain levels, fall into that.
I would speak with a recruiter and attempt the ASVAB to see your options.
Our bootcamp in 8 weeks, but I am unsure of specifics on how long the following CS A-school is.
As for being a 'chef'.....you would generally start off as a 'food service specialist' which in humble terms is the equivalent of a short order cook/food prep assistant. As stated earlier, you would generally attend 8 weeks of basic training and 8 weeks of specialty skills training. (This may vary between branches) The hours are long, the conditions are hot and other Soldiers may harass you for 'just being a cook'. With that said, I can tell you that feeding Soldiers is the MOST IMPORTANT task required to keep morale high and keep Soldiers moving. Food service specialists provide hot meals to hungry Soldiers, they keep feeding stations sanitary and they help combat vermin and disease in the field. Becoming a food service specialist does not require any specifically high ASVAB scores, but it is one of the most important jobs in the military. The Army marches on its stomach.
On a side note, one of my best friends was a Food Service Specialist. This guy can make a meal fit for a king from yesterday's scraps. He made Army chow exciting. We all looked forward to eating his food. Don't ever let anyone discourage you from 'just being a cook' in the Army. It's an incredibly rewarding job.