The dual LED flash in the iPhone 5s allows changing its color from white to amber, to approximate the color temperature of ambient light. dpreview.com writes:
In fact, it features the first auto-color balancing flash of any camera. The light from a flash, LED or otherwise, is rarely the same color as the ambient light. This is particularly true when shooting in the warm tungsten light typical of indoor, nighttime scenes. With different colored light sources, white balance is almost inevitably going to be wrong for at least part of the image: the flash light may look bluish, or the ambient light may look orange.
This makes me wonder:
Is there a similar device for the hot shoe of a conventional camera?
How it could look:
Dual LED flash like on the iPhone, for near distance shots.
Or: A conventional flash with a color LCD on top. If the LCD is RGB, then the intensity of the flash would go down to one third its original intensity, approximately: red sub pixels discard green and blue photons, green sub pixels discard red and blue photons, etc.
A compromise could be to use an LCD with just two colors. Part of the sub pixels would be yellow, allowing transmission of red, green, and yellow photons. The other sub pixels would be blue. Ideally, intensity would go down by just 50%.
Or, as @EdgarBonet proposes below, use orange (or yellow, amber) plus white sub pixels.