I'm glad you're taking my feedback! I don't know anything about flag design, but since many pride flags (for example the rainbow flag, the bi pride flag, the trans pride flag...) contain additional colours to the standard colours you mentioned I'm not sure it's important in this case.

So, what colour? I'm not sure about white, which I tend to associate with purity, absence, death or surrender, and none of these colours make sense. The idea of keeping it in black is interesting, but at the same time it sets it apart quite a bit, I'm not sure I like that. How about purple? It combines the colours of physical disability and mental illness and many people with chronic illnesses see their mental health affected as well as their physical abilities. By the same token, you could also go with orange because a lot of people with chronic illnesses experience memory and concentration problems. Also, I like purple and orange.

Of course, these are only my humble suggestions, maybe finding a few more people with chronic illnesses to talk to would be a good idea.