我可不觉得 - agree or disagree? I worked with dialogue of two persons:  

A: 外边下雨. 挺有意思.
B: 我可不觉得. 上个星期我穿了新衣服出门, 忽然倾盆大雨. 我的衣服报废了.  

可不 - vocabulary translation gives "1) that's just the way it is. 2) exactly".
But here Person B is complaining about the rain and spoiled clothes. So does Person B agree with A?
Or may be "可不觉得" here is a short form of "可是 不觉得"?
The same as "I don't think so".

我 **可**(means emphasize) 不觉得
我不觉得
不觉得
不


When it's a single word "可不", as you post, it is an interjection often used when spoken; it means "exactly" or "you're right".

For example:

你真帅
那可不


And there won't be any usage of this meaning in the form of "我" + "可不",  especially when they are two characters behind "可不". 
Just remember the usage scenarios of oral language like this (a sentence only has 3 characters).

And why can this negative word be used to represent approval?
This is called 反诘 ("rhetorical question").