When you add NaCl in water you notice that when the water boils over, it causes the flame in the gas burner to turn bright orange.
My question is how would you explain the appearance of the color in the flame?

Ahh when a gas flame is orange it means that the burning reaction is incomplete and cooler.

The water will be cooling the flame and therefore causing combustion to occur at a lower temperature thus emitting lower energy spectra and the incadesent material floating within due to incomplete combustion will result in the red and orange colour.

Hope this explains it a bit!