"I got the feeling that..."
Usually Chinese people say 我觉得 or 我感觉, meaning "I feel":


我觉得你的英语比我的中文好。
我觉得今晚一定会很棒。
我感觉他们会否决我的提议。


Or you can use the structurally similar 我有一种感觉. It sounds more lyrical, and is less commonly seen:


我有一种感觉，那就是今晚一定会很棒。
我有一种感觉，如果我你逃课的话，老师发现会很生气的。


--

"I got a bad feeling about this" is a different thing. If the thing has not happened, then it's usually "我有一种不祥的预感" or "感觉不妙啊". Most Star Wars references could be translated this way.