No, it's not a common phrase at all. In normal English usage, it seems rather strange and not a typical expression you would hear in everyday conversation or see in general writing.
I'm not sure specifically which 'black cock wife story' you are referring to. There could be many fictional or cultural stories with this name. Without more context, it's difficult to say what it's about.
There's not enough information in just 'sucking cock camping story' to accurately say what it's about. It could be a really creative and unique camping story where 'cock' refers to something like a water faucet or valve (in a non - vulgar sense) and there is a situation where it seems like something is being'sucked' in a mechanical or natural process during a camping trip.
No, it is not at all appropriate. We should uphold good moral values in our communication and avoid promoting or spreading any form of vulgar or improper content. Society has standards of decency, and this clearly goes against them.
Well, without proper details, it's difficult to determine what this 'cock sucking challenge story' entails. It could be a prank story, or perhaps some sort of made - up dare among friends that got turned into a story. But again, this is all speculation without more information.