I strongly disagree with Dr. Vernon. Many ME/CFS patients have adverse reactions to vaccines. The question here is an individual benefit-to-risk decision for you personally (and may be different for each vaccine):
is your specific chance of getting a flare, and the severity you think it might be, worth the chance of possibly preventing the specific disease the vaccine is preventing (should you happen to be exposed) and the severity of that particular disease and availability of other treatments.
If one has had bad reactions in the past, the chance of having a bad reaction again is greater. If one has had vaccines without incident, the chance of having a bad reaction is less. If one hasn't tried it, one doesn't know and must judge only by the items on the vaccine and disease side.
For you, BEG, since you already had a reaction to a flu vaccine, the risk portion of the benefit:risk ratio goes up (there is more risk for you). If your doctor cannot understand this, you might need to consider looking for a new doctor, but that's a bit complex depending on what other support and understanding your doctor has about other things related to your disease.
One place where an official recommendation for being careful with vaccines can be found is at the Allison Hunter Memorial Foundation on the
fact sheet. This states that patients may fail to 'seroconvert' (or produce antobodies against the organism being vaccinated against, which is the whole point of vaccinating - in other words, the vaccine may even not produce immunity). Unfortunately there are no footnotes; the citations are just all listed at the bottom, so it's difficult to figure out what study this is taken from.
The new IACFSME primer may have mentioned that, too - I don't recall offhand.