They are both correct but have different meanings. It's no good (doing something) .. is an idiom that means there is no point or use in doing it; you are wasting your time doing it. For example: It's no good asking him for help. He's too busy with his own work.
Similar examples from Google:
It's no good asking – no one knows what it is and where it comes from.
It's no good asking them anything, they couldn't care less!
It's no good asking me. I haven't got a clue.
On the other hand, It's not good (doing something) .. means that it's not a good idea to do it. For example: It's not good asking him for help; he will think you are incompetent.
More Google examples:
It's not good asking that, here on the internet, because there are many people, who will try take you down.
It's not good asking to move deadlines because, as a freelancer, you lose credibility.
It's not good asking strangers health related problems, better consult the professionals.
