I do appreciate your reading the board and trying to do your homework, but I think that you are a little off line. Since this is for exterior painted brick, Zinssers' B-I-N which you probably saw in most of the posts you read is for interiors. Their 1-2-3 is probably a good choice but you hired your painting contractor for his knowledge and experience as much as for his ability to swing a brush. There are so many local conditions and situations that occur across the country that there is no one answer for everything. If you did your homework in choosing him, you should listen to what he has to say. This does not mean that you can't talk and work with him to be sure that he understands the kind of job you want done.
How much of the old flaking or chipping paint is he going to scrape? Did he understand when he quoted the job that would last for many years and that you were willing to spend a couple of bucks more to have it done right. If you told him that you wanted the lowest possible price on the job, and he quoted using materials and practices to get it, would it be fair to come back now and demand premium materials at the same price? I don't know if this is the case, just asking. But you should be comfortable enough with your contractor to discuss these issues, listen to his comments, and decide whether to stay at the quality level he quoted or tell him to move up a step or 2 and that you will pay for the better job.
Among the many things that we don't know is how long the "several years since the last paint job" really is. And we recognize that you might not either. If it is 2 or 3 years, that could be the result of poor or cheap jobs in the past which will lead to rapid deterioration of this one too. For about everything, a good strong foundation is important, including paint. If the foundation is weak, just adding more to the top will not let it be a new paint job for long.
This might not be what you want to hear, but it is the info that you need to make the right decisions.