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If you know the composition of any sample of compound, is it possible to predict it's flame test color?

For eg, if you can given Sodium Chloride, then without actually doing the flame test, can you mathematically (and using physics and chemistry obviously) come up with it flame color, ie yellow-orange?

Do the flame test colors follow any pattern for different metals? (for eg, does it follow the spectrum?)

Does the group (for eg alkali metals or transition metals) affect the flame color?

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