“听出” cannot be used to describe smell or flavor.

If you need to describe those elements, you could use the verbs “闻” (to smell) or “尝” (to taste) to replace “听” (to hear, to listen), as the answer of @Kiet Bach suggests.

In addition, if you are translating a literary work (an online novel I guess? according to your description), you could use a wider verb "sense" in this context. I think the author may want to write about the fact that, the protagonist "senses" something shabby or makeshift through the speech on the phone. But anyway, the collocation “听出...的味道” is questionable and will be considered an error in more formal texts.

Chinese term (edited): 听出...的味道

“听出....味道”是完全可以的，因为这里的味道不是指用味觉去感知的味道，像酸、甜、苦、辣，而是指“意味”，“含义”，“风格”等等。是味道的figurative 用法。

例如“从她的话里我听出了讥讽的味道”。
以下是几个网站搜到的：
听着熟悉的歌却听出了陌生的味道
-百度
《醉乡民谣》主题曲《500 Miles》, 听出人生的味道！
-搜狐

一首欢快纯音乐《夜、萤火虫和你》，意境唯美，听出夏天的味道
-Bilibili

味道 can refer to the indication of something. For example, 他的话带有讽刺的味道. His words have a smack of sarcasm.

For your reference only.

No, you should not use for 听出 for smell or flavor.

Do you smell something bad?
你闻到臭味吗？

Are you able to taste the strawberry in the cake?
你尝到蛋糕里草莓的味道吗？
你吃出蛋糕里草莓的味道吗？

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Note added at 4 hrs (2022-08-20 02:54:39 GMT)
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Correction (extra "for"):
No, you should not use 听出 for smell or flavor.


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Note added at 1 day 15 mins (2022-08-20 22:51:32 GMT)
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Some have suggested that it could have been a figurative use of “味道”。 I agree that it is a possibility. If so, “味道” just means "feeling". For example:

我从这首歌里听出悲伤的味道。
I can feel a sense of sadness listening to this song.
(Literally: From this song I can hear the taste of sadness)

"听出" normally goes with a quality/feel discerned from a sound, and "味道" is used figuratively here to refer to that quality or feel.

It means the listener picks up a note of something.