since different gases give different color when burning, how can we know that the red colour we obtained is not just the actual color of gases burning, but rather a red shift?
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The Doppler Effect is a well studied and understood phenomena. Basically the motion of an object affects how we perceive things from it. Wavelengths appear to be higher when the object is moving towards you and and when something is moving away. You experience with sound wave: the pitch of the sound of a car is different when it is moving towards or away from you.
Since materials produce and reflect very specific frequencies of light even when they are in high energy & gaseous states, we can use that as a reference points to determine how fast an object is moving. Even in the sun, there are several different specific frequencies in the light we can see that tell us what materials are inside it. It’s not a case of there just being one wavelength being produced, but several.
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