ような気(き)がする is a phrase that takes the base meaning of 気(き)がする ‘to have a feeling that (A)’, or ‘to give off a vibe that (A)’, and adds an extra layer of uncertainty through use of the 助動詞(じょどうし) (auxiliary verb) よう. This can be understood as meaning ‘to have a funny feeling that (A)’, or ‘to kinda have a feeling that (A)’.
As always, よう must be attached to the 連体形(れんたいけい) (attributive form) of any word that comes before it.
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あの技(わざ)はなんか簡単(かんたん)そう。俺(おれ)でも出来(でき)るような気(き)がする。
That technique looks easy. I feel like I would be able to do it.
そこへ一人(ひとり)で行(い)くのは危(あぶ)ないような気(き)がする。ガイドと一緒(いっしょ)に行(い)った方(ほう)がいいと思(おも)う。
I have a feeling that it would be dangerous to go there alone. I think it would be better to go with a guide.
あいつと話(はな)した感(かん)じでは元気(げんき)なような気(き)がするけど…
Based on talking to him, he seemed like he was doing well, but…
前(まえ)にいる人(ひと)は警察(けいさつ)のような気(き)がする。
I have a funny feeling that the person in front of us is a cop.
気(き)がする is quite a bit stronger than ような気(き)がする, so the latter will often be used when the speaker is not 100% sure about something, and does not want to sound rude.