Colloquial auxiliary (from …te + iku). Attaches to the -te form of a verb to indicate that an action or state continues or a change will proceed from now on.
最近、体調がどんどん良くなってくよ。
Lately my health keeps getting better.
このまま手を加えないと問題は大きくなってく一方だ。
If we don't do anything, the problem will only get worse.
彼女は毎日練習して、どんどん上手くなってく。
She practices every day and keeps getting better.