We often associate empires like Rome and Sparta with the color Red or Macedon with purple. Did these nations have a single color that represented them in battle or politics? And if they did what were the ones that they used?
While a given empire did not exactly have a colour in China, the Emperor/s did. Yellow has historically been the colour which represents royalty. Under the Qing, the highest ranked in the Banner system were the yellow banners. The flag of the Qing is also yellow, and the emperors would often be dressed in the colour.
The mythical emperor who is ancestor to China is the Yellow Emperor. The colour had important metaphysical symbolism. In Nanjing, after the death of Sun Yat-Sen in the 1920s when his mausoleum was being constructed, there was talk about the colour of the roof tiles (blue) and the significance that they were not yellow, as they would be for the emperor. This has significance for him as a figure of republican reform and a move away from emperors. Ironically his memorial hall in Taipei has a yellow roof anyway.
So while in China a given empire did not have a national colour in the sense that you're asking about, the notion of empire certainly did.
Rome didn't necessarily have a colour, but particularly in the Republic the idea of Rome was often embodied by the toga and the purple stripe(s); if you saw a man in a purple-striped toga with red-robed lictors carrying their fasces, you would be seeing 'Rome'. The combination was picked up by the Empire with the purple robes of the emperors and red or purple cloaks of their guard.