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According to コトバンク, 旗色が悪い can be used when there is some connotation of a battle, war or fight - which makes sense because it literally translates to something like the color of the national flag is bad.
Just wondering how natural it would sound in more general contexts of failure or despondency. For example:
私の商売は、大損失で旗色が悪くなった。
Here's the list of examples from BCCWJ.
We can see the idiom 旗色が悪い can be safely used in non-military contexts, but is always used in the context of argument, debate, competition, or at least comparison of two opposing ideas. It should not be used to describe simple failures without competitors, rivals, enemies, etc.
I feel 私の商売は大損失で旗色が悪くなった on its own sounds a little unnatural because there is no direct reference to comparison in this sentence. It should be okay if a competitor has been mentioned in previous sentences. Something like 我が社はA社とのシェア競争において旗色が悪くなっている is fine on its own.
Now, let's check what 旗色｛旗色｝ be translated in English.
Weblio says,
(wait to) see which way the cat jumps
The odds are in his favor [against him].
So, 旗色would imply which "side" might be a winner.
Therefore, your,
私の商売は、大損失で旗色が悪くなった。
misses a something, which is the very "opponent".
Imagine when you are in the battle which flag seems to be "decisive" to that one.
Your business might might go under, but still the sentence lack the reference to the competing sellers.
