ano ko ga futteita makka na sukaafu
This is a part of lyrics of an inserted song to the animated movie Space Battleship Yamato (Japanese: 宇宙戦艦ヤマト Uchū Senkan Yamato, also called Cosmoship Yamato).
Not only I but most Japanese don't think the given phrase means ano ko ga makka na sukaafu o futteita.
It is a part of an apparently unfinished sentence but it is considered a part of a sentence omitting the important rest of the whole sentence, therefore the phrase itself gives us who read or sing it room to image.
The room would be filled with various things basically depend on the context surrounding the phrase and more importantly depend on the ability of the recipients.
Before I read the whole lyrics of the song, I imagined the whole or the complete sentence including the phrase might be like:
- 私はあの娘が振っていた真っ赤なスカーフが忘れられない。
I can not forget the bright red scarf that the girl was waving.
or
- 私はあの娘が振っていた真っ赤なスカーフが目に焼き付いている。
The bright red scarf that the girl was waving is branded on my mind.
"ano ko ga futteita makka na sukaafu" is gramatically correct?
Yes, the given phrase is gramatically perfectly correct as Japanese and it uses a technique in rhetoric, called a [体言止め]{taigendome} or "substantive stop" (to use a noun in the end of a phrase omitting an important part like a predicate or a verb), which gives the phrase momentum, reverberation and gives room to think.
As for ko, there are roughly three ways to use in Japanese.
The First one is very common. When you point your finger at a boy or a girl around under 10 to 12 years old, you would say "ano-ko or that kid/child".
The second one is used, when parents, especially a mother, talk about their son or daughter, even how old the "ko" may be, in a phrase such as: "ano-ko wa ima nani o shite-iru ka-shira?" "What is my son/daughter is doing now?"
As for the last one, ko in ano-ko in the given phrase, it means a girl which is written 娘 not 子 in kanji.
There is not any rule neither in kun-yomi nor in on-yomi for 娘 to be read as "KO", I think, but we write "あの娘" and read it as "ano-KO" habitually.
Usually ano-ko is a set phrase which means that girl (あの娘 or あの女の子) not that child/kid (あの子), which is a girl as an object of love.
Lyrics
真っ赤なスカーフ
あの娘がふっていた
真っ赤なスカーフ
誰のためだと 思っているか
誰のためでも いいじゃないか
みんなその気でいればいい
旅立つ男の胸には
ロマンのかけらがほしいのさ
ラララ...
ラララ... 真っ赤なスカーフ