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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Occam’s razor.
Gases give of specific frequencies of light and not he full spectrum. To the naked eye it just looks red or grenn, but if you break that light up to see the spectrum there are only a few specific wavelengths present. This light is caused by electrons hopping around in the atoms electron cloud.
When we look at distant galaxies we see the same spectrum but it’s shifted-almost always in the red direction. That tells us either
1. The galaxy is made of the same stuff we see here on Earth that’s emitting light in ways we understand. It’s just moving and making that light redshifted
2. The galaxy is made of some new unknown substances that is behaving in some unknown ways that only appears to mimic a collection of gases we know all having the same motion to shift the light.
That’s where Occam kicks in and we say the second explanation has more complexity because it need an entirely new substance in addition to our familiar matter as well as all the new ways it interacts to emit light while the first theory say that stuff we already know is doing stuff we already know it does. So we go with theory #1.
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