I'm going to assume that since you're on this site you're at least 18. That being said it should be legal for you to buy your own negating the necessity of telling your parents.
If money is an issue, spend some time browsing the site, speaking up in the forums, commenting on reviews, searching for products, and adding things to the compare list. You get points for these actions which can be used to buy a packer, it shouldn't take you long unless your after Mr. Right but even then it can be done.
If you're wanting to tell you parents because they are supportive than it might be slightly uncomfortable but not difficult to bring up. Start a conversation about the tools guys use to make their appearance more gender appropriate. I would start basic with things like haircuts, clothing choices, then to binders, then bring up packers. "...binders help hide the bulges that shouldn't be on my chest, and there are things to help make bulges that should be there..."
I wouldn't dream of bringing such a thing up with my parents even though I've seen the questions/look on my moms face when I visit for dinner in the tighter jeans I wear when I go out for the night.
Congratulations on having such an open relationship with your parents that you would even think you could bring it up with them!