The two primary ways I know of to get to any career are either by education or experience. The most common route nowadays is a formal education - go to school or take training courses to show that you have the abilities required to do a specific job. It sounds like your friend has tried this route and was not successful.
You can also seek training courses - either online or in person - that don't require applying to get in. These are usually of a lower quality than going to university and won't be useful on their own, but they are still valuable to get you started and help you get a job.
The other method is to start from the bottom up and get on-the-job experience. Find a chef or cook who is willing to take on your friend as an apprentice cook, or even a dishwasher, with the goal of gaining real working knowledge and working up the ranks. This method certainly takes longer and may be less rewarding when you start, but it is definitely still valuable. A downside is that some jobs will just not be available to someone who doesn't have the formal training.
If your friend's career as an apprentice is progressing at a rate he likes, then he can continue down this path to gain the informal training he needs to become a chef. If not, he can always go back and reapply to the formal education programs, and maybe having the real world experience will now help him on the exams. He can also still continue to seek out the individual training courses to augment his job experience and give him a leg-up on his coworkers when it comes time for advancement.