It's an issue of width.

Single-speeds/fixies use I believe the oldest chainwidth standard, same as the old ten-speeds (5 cogs). As manufacturers squeezed more and more cogs into cassetes, up to 11 now, the spacing got narrower, and the chains had to get narrower. A colored single-speed chain would not fit between cogs to drive your rear wheel. Unless you could find a presumably 6-8sp chain that was colored, but as PGRS noted, colored chains are typically blingy fashion accessories for hipster ss/fix bikes