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.