Just because an individual has an immunity (whether acquired or natural) to a disease does not mean that a practical vaccine can be manufactured based on that individual's biochemistry. If Cole does have antibodies to the virus, it might be possible to produce a vaccine that caused people inoculated with the vaccine to produce identical antibodies, but that would be exceedingly difficult. It would be necessary to reverse engineer an antigen that would cause people to produce the exact same antibodies, an extremely challenging task. Moreover, this would only be possible if Cole's antibodies to the virus could be isolated and identified to begin with. Cole will have antibodies to thousands of different pathogens in his system, and picking out which ones were responsible to his immunity to the engineered virus would again be hugely challenging.
So having somebody who is immune does not necessarily give you an easy path to making a vaccine. Of course, it's probably best not to think to hard about this anyway, since the movie's explanation for why they couldn't make a vaccine in the future (that they needed a sample of the virus before it mutated) does not make any sense either.