Where do you get your information that people with schizophrenia live longer than other people? I don't think it is true. For one thing, the suicide rate is about 20 times as high as for the general population.
Flax oil is very good and helpful but it does not help everyone, and certainly more is needed than just flax oil for most people. My son has taken Essenial Balance, which is a mixture of flax and some other nut and seed oils, for almost a year, plus a fish oil product, and as far as I can tell they haven't helped his symptoms. But I will keep giving them to him because his essential 3 and 6 oils were very low in his lab tests.
Niacin 2-6 grams for most people and vitamin C 5-10 grams a day are two of the most important supplements for schizophrenia, but there are quite a few others that are helpful, including the essential oils.
What you said about finding food allergies is very true. There is a book called Brain Allergies that covers this subject very well.