Ever since the dynamic weather and lighting update, rainbows went from rare to essentially non-existent. (They used to occasionally appear after switching from rainy to sunny, even looking at a distant gym).
But I saw one today! I noticed it in a Rocket Battle and spotted it on the map, but not on the encounter screens.
Some strangeness: It was VERY brief, as you can see in the last two images. This was also my first login of the day, and for some reason I noticed my Daily Adventure Incense didn't appear until a restart (which I only did after the rainbow was gone).
The actual weather shift was cloudy to windy. The cloudy weather had a bluish background though, so it might have been one of those psuedo-rainy ones.
by TheMadJAM