I would like to know what the original context was. It seems to me that the person is emphasizing that something is not debatable, not able to be changed. We can use "period" to say that there is no debate about something—this is a way of emphasizing it: I won't eat anchovies, period. English people might use "full stop" in the same way (I would get a second opinion on that one. "Point blank" means you've stated something very bluntly, without trying to be nice. So together "point blank period" probably emphasizes that something was said without the possibility of further discussion/debate.

"I'm not going out with you, point blank period!"

I started to answer this question by saying that it didn't sound right. But from a web search I have learned that it is a relatively new expression that has entered the language. It is an expression unfamiliar to me, so I'd better not try to explain it. Just be aware that it is IS a new expression.