Block user's stream

How do I block user’s stream if that user broadcast inappropriate content? Is there any API or SDK that can help me?

Depending on where you are getting stream information to start with, you probably already have the data.
Both channels and streams API return a mature tag with false/true.

EDIT: actually, there might be a null instead of false.

what does mature flag mean? Does it mean that the user is streaming some inappropriate content?

It means that the broadcaster has tagged the stream as it might contain mature content.