My understanding is that the only reliable way to look for food intolerances is an elimination diet followed by reintroduction ‘challenges’ of individual food stuffs.
To do this systematically is very time consuming, you are talking about years. Consequently it makes sense starting with those food stuffs that are known to cause problems for us. There is not much good research out there but we seem to be talking about gluten, lactose, caffeine and alcohol most commonly. For example, in the region of between 10 and 25% of people with ME seem to have [non coeliac] gluten sensitivity, so the numbers are not insignificant and the whole topic really needs a more systematic investigation, and everyone with ME should have access to appropriate advice/support. This is a big area where the so called specialist ME/CFS services, at least here in the UK, have let us down.
One thing also to bear in mind is that the relationship between symptoms and food stuffs may be more complex than you might first think. For example one food stuff may cause inflammation of the gut mucosa, which triggers a ‘leaky gut’, which in turn allows other food stuff into the blood stream triggering other symptoms. So symptoms beyond gastrointestinal ones, such as migraine or skin conditions or brain fog, may require a combination of food stuffs.
Further, unlike allergies food intolerances seem to be dose dependant, that is the symptoms have a direct relationship to the quantity of the food stuff consumed. I don’t know if there is any research on this in relation to intolerances in general. Also I have read, but again don’t know if it has been researched, that food intolerances are more likely to appear or even disappear overtime, whereas allergies are relatively more consistent. This may mean that even if you identify your pattern of sensitivities at one point in the course of your illness, it may no longer be relevant at another stage.
Certainly my gluten intolerance has changed over the last twenty years. At first I could not cope with any form of wheat, even spelt, but could cope with rye. Rye has gluten, but in a different form to wheat, or so my godson who is a Konditor (between a confectioner and a pastry chef) tells me. However over a number of years my tolerance for rye deteriorated and now it causes the same problems as wheat at the same quantities. Further my gluten intolerance [probably] started at or around the onset of my ME, though it was only identified some years latter, but my caffeine intolerance did not begin until some fifteen or more years into the condition.
One thing to bear in mind too, is that there may be a time lag between ingesting the trigger food and the appearance of symptoms. For example for me gluten triggers a migraine, but twenty four hours later. When last in Germany I foolishly had falafels in a Turkish restaurant, but did not bother to confirm they used only gram flour. Twenty four hours later the migraine hit. However my caffeine triggered migraines emerge only six hours after consuming it.
[Added - it would also in interesting to know if the food intolerances of people with ME behave in a similar way to those occurring in the general population. There is some suggestion say that POTS in the general population predominantly effects younger women and usually spontaneously resolves, but that this pattern is different for POTS in the ME population. Is there a similar divergence with food intolerances?]