External justification in The Man from U.N.C.L.E

It's possible they were left in, as they were aiming to have lens flares elsewhere.

Visual effects supervisor Richard Bain and visual effects producer Sarah Tulloch, who worked on the film, explain in the article Crafting the Killer Chase: The Man From UNCLE that lens flares were recreated digitally for a car chase:

In delivering the visual effects for the Berlin scenes, Rise matched the look of the original anamorphic plates which often required extensive flare and distortion effects. “For instance,” outlines Gellinger, “we looked at the practical car headlight flares and re-created those as NUKE flares in a custom script. We roto’d out every single disc and ray that was in the real plates and turned them into little 2D sprites that we could manipulate in our custom flare and track them onto our CG cars. That really paid off. We had four re-created practical flares in our NUKE gizmo that we could apply depending on what lens was used.”

Given that Ritchie approved intentional flare in the car chase, it's possible that either he didn't mind natural flares created by the lens, or wanted flares adding specifically.

Given the film is set in the 60s, it seems more likely that lens flare reflects the quality of films of the day, rather than any other hidden meaning.

I don't think that the rainbows were meant to indicate any sort of meaning. Rather, they are lens flares, they either happened organically during filming or were added later on to give the movies a slightly more "rustic" feel.

Lens flares occur when light, usually strong light, hits the lens of the camera at particular angles. Back in the day it was a lot harder to prevent these, but as technology has progressed they have become easier to prevent. It has become a thing to re-add lens flares to make things seem more authentic or older.