"ガキの使い" is just one of Japanese slang. You could say "使いっ走り" or "パシリ" as well. I think that means "to run an errand". You may translate "errand runner" in English. (cf.) https://www.youtube.com/watch?v=96krIfKT1Ic I would say this is exactly ガキの使い. 「ガキの使い」とは日本語の俗語（スラング）の一つです。「使いっ走り」や「パシリ」とも言います。 意味は「to run an errand」だと思います。英語では「errand runner」と言ってもいいでしょう。 （参照）https://www.youtube.com/watch?v=96krIfKT1Ic これは正しく「ガキの使い」と言えるでしょう。

It's translated into "errand brats." But "ガキの使い" is shortened from "ガキの使いやあらへんで！", which is translated into "We aren't errand brats!." Hope this helps you.

がきの使い is used only in the phrase ガキの使いじゃない. You can replace the end of phrase じゃない to other similar meaning ones like ではない, ちゃうで( Kansai dialect) , と違う. がきの使い implies that an inexperienced yet-not-grown-up boy/girl can only do just a thing what he/she is told to do. For a typical example to do this phrase, it is a pay-back-money situation. An evil outsider visits a man and calls to pay back his money, but the debt man have no money and he says he can't. The evil threatens the debt man and then he just says 私もガキの使いじゃないから、払ってくれるまでは帰らない. He intends to do anything to get money. But the title doesn't mean anything. I guess it is because the phrase is so funny that we don't use in our own, and we only see it in such movies like violent gangsters actions やくざ映画.