Does working out help mens chest hair growth?

Unfortunately chest hair growth/pattern has to do with genetics and nothing else: there is nothing you can do to get more chest hair to grow, and the only way to reduce chest hair permanently is electrolysis or laser hair removal.

Most men don't realize it, but their body hair keeps growing in throughout their 20s; if you are genetically predisposed to have chest hair, it might start growing in when you are 16, 25, or 30. It just depends. Men with light chest hair in their teens and 20s may find in their 30s that their chest hair gets denser or more widespread.

The best gauge is to look at your father, brothers, grandfathers, and uncles: if they have chest hair, you probably will too.