You might be surprised to learn that out of the many suits Batman has, he actually owns a Rainbow-colored one – and there’s a pretty legit reason behind it!
The Rainbow Batman suit first appears in March, 1957, in issue #241 of Detective Comics (Volume 1). In it, the first Robin saves the life of a girl in his civilian guise as Dick Grayson, but injures his arm. After the incident, Batman wears a variety of different colored suits, culminating in the rainbow-colored one. The bad guys are, of course, captured and Batman returns to wearing his normal suit. He then explains to Robin that he wore those colorful costumes to distract the public from Robin’s noticeable arm injury; which could be linked back to Dick Grayson since he received widespread media attention for his heroic actions.
The Rainbow Colored suit has since made several appearances, including as a toy figure, in the Batman: The Brave and the Bold cartoon series, and in the 2016 Trinity series… where, thanks to being retconned by the Crisis on Infinite Earths crossover, Bruce Wayne vehemently denies remembering the incident.
And there you have it.