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.