I definitely have to agree with The Duke on this one.

With the "unmade fire " The "speaker" obviously tries to expresses that the potatoes were put under the fire BEFORE it was lit. Just imagine trying to trap potatoes under an already lit fire.

“pluck them out of the cooking embers ” sure means that the fire is already lit, but it wasn't lit when the potatoes where put there.

Although I've never heard of an unmade fire and can't find any references to such an expression. It seems a much better guess that it's meant to describe an unlit or perhaps unbuilt fire, rather than an unmade fire as in an unmade bed.

抱歉，我粗心了。
Chenxi 分析得对。

unmade fire 是还没有生火的炉火堆。
这里，fire应该是表示位置，但又不同于火炉 fireplace。

 

我 Google 到了这么一句话，可以说明它的用法：
Gregg grabbed the tool and together with Grandad the pair held it and bent and lit the unmade fire. Immediately blue and yellow flames roared into action.

 

下面是我原先的答案：

我不同意The Duke 的分析。
“pluck them out of the cooking embers ”说明，火已经熄灭了，而不是尚未生火。

unmade 在 unmade fire 里，应该和在 unmade bed 里是一样的，表示（在用完后）没有收拾好、没有整好。
正如起床后应该收拾床，烧完柴火后应该收拾灰烬。目的都是为了保证日常重复利用。当然，在野外临时点的篝火，大概就不需要收拾干净了。

I've never heard that phrase before, but the 'speaker' means, the fire that hasn't been lit yet, the fire that isn't burning yet, the fire that hasn't been BUILT yet.  I think that the most standard and formal way of saying 'get a fire burning in a fireplace or stove' is 'BUILD  a fire', but the character in the quoted story is obviously not a speaker of modern standard English.