From two substances this happened to me, which won't apply:
a hyaluronic acid injection in my spine once and
now using "flush" vitamin B3/niacin when I increase the dose, much more slowly now.
So praps using the term "flush" can help you get closer to the reason....
buoyhealth has a good long page about facial redness.
Of the possible reasons named there, I can imagine an allergic reaction and an infection most likely, since it sounds like you have had anything serious checked, as advisable.
An infection itself you'd probably "feel", whilst you might find a food, med or contact trigger.
I have a pre-form of atopic dermatitis without any visible signs, but this is something that can be triggered by stress, like in the flare. In my case even water is a trigger as well as soaps etc.
So it may be one or a combination of triggers as a result of a flare.
The other way round might be an autoimmune process, as a part of fibro or something separate. And not necessarily one of the typical ones that have been identified yet.
So prevention might be trying to find and eliminate triggers as much as possible and alleviation taking (more of) something anti-inflammatory.
(The more well-known anti-inflammatory supps would be ALC, D3, ginkgo, mag threonate, NAC, Ω3, CoQ10, rhodiola, SAM-e, zinc, ALA, there's 20+ more I take most of, incl. the spices I don't tolerate/take.
For anything feeling inflamed 15-30 seconds of cold water helps me, despite more water inflaming).