What do the words 「きてやった」 mean?

Question

It is a situation that a little girl throwing several raw eggs to two policemen. After that, she was running away and saying the below sentence.

Here is the sentence.

なっとうもふりかけてきてやった

Answer 1

ふりかけてきてやった is composed of three verbs, ふりかける, くる and やる.

振りかける is an ordinary transitive verb meaning to sprinkle. くる and やる are called subsidiary verbs (補助動詞), which are already explained in detail here: What is a subsidiary verb?

The subsidiary verb くる has several roles, some of which can be a bit tricky at first. From デジタル大辞泉:

９ （補助動詞）動詞の連用形に接続助詞「て」が付いた形に付く。
㋐少しずつ移行したり、程度が進んだりして、しだいにその状態になる。だんだん…になる。「日増しに暖かくなってきた」「最近太ってきた」
㋑ある動作・状態が前から続いている。ずっと…する。…しつづける。「再三、注意してきたことだが」「改良を重ねてきた品種」
㋒ある動作をしてもとに戻る。…しに行って帰る。「買い物に行ってくる」「外国の事情をつぶさに見てこようと思っている」
㋓ある動作・状態をそのまま続けながら、こちらへ近づく。また、そのようにしてこちらへ至る。「敵が押し寄せてくる」「付き添ってくる」

㋐ is interesting (see the link), but it's not relevant now. The girl used くる in the sense of ㋒, because she had done it somewhere else. くる in the sentence in question simply means "go/come and [verb]", "[verb] before coming here", etc.

As for the subsidiary verb やる, there are two meanings:

15 （補助動詞）動詞の連用形に「て」を添えた形に付く。
㋐わざわざあることをしてあげる気持ちや恩着せがましい気持ちをこめて、目下の者のために何かをする。「相談に乗って―・る」「勉強をみて―・る」
㋑積極的にそのようにする。ことさらにそのようにしてみせる。「飛び降りて―・る」「舌をかみ切って―・る」

Again, ㋐ is common, but the definition ㋑ applies in this sentence. I think it can be translated into English as "dare to [verb]", "[verb] purposely", "even [verb]", etc.

All in all, this sentence means "I even sprinkled natto (on the policemen, before I came here)!"

Answer 2

きて = くる = come
やった = やる = do
きてやった = came and did

So that's what those two mean by themselves. However, there is also a verb in the て form before that. て + くる form can mean "come" in time as well as space:

もってくる = bring
やってくる = do (until now)

The second meaning is the opposite of temporal て + いく:

やっていく = do (from now on)

Also, やった can have a jubilant connotation, like shouting "I did it!" "やった!" Which still makes sense with the literal translation, but I just thought I would mention it, because it's one of the ways that やる is different from する.