No not that kind of fire, although we've had more than our share of wildfires here in Southern California the past few weeks (and thankfully everything seems to be under control now). I actually never heard the term "fire rainbow" until recently, but it seems it is now a commonly used term for iridescent clouds, coined by a journalist after a spectacular display in Spokane, Washington in 2006. A catchy name, but they have nothing to do with fires and they aren't a true rainbow, which is caused by refraction. Iridescent clouds can form when wispy high altitude clouds made of very tiny ice crystals or water droplets are perfectly aligned to diffract sunlight. They are most likely to occur in newly forming clouds when the droplets are most uniform in size.
Luminescent clouds that I've seen in the past have been the typical pastel pink and green at the fringes of the clouds. This is the first time I've spotted actual rainbow colors and I believe this was actually a circumhorizontal (or circumhorizon) arc, especially because of the shape of it when I first spotted it. Because the phenomenon only occurs when the sun is at an altitude of 58º or higher they are considered to be relatively rare. For the US in general we're limited to about 6 weeks on either side of the summer solstice, which is June 21. Keep your eyes open and look to the sky over the next few months, especially around noon when the sun is highest in the sky.
By the time I spotted the beautiful colors, ran inside to grab my camera, changed the lens and ran back outside, the clouds had already moved enough that the rainbow colors were shifting and not as visible as they were when I first spotted them. I still wanted to grab a shot because it's something we don't see very often.
The world is full of beauty if we just take the time to look.