I've been wanting to flatten my chest extremely badly so I don't have to wear my hoodie every day and feel uncomfortable. I'm not too sure if my mom really knows what binders are... I mean, she does know about transgender stuff, just not... that much. Is there an easy way to ask her?
If you don't want to come out then I'd just say you feel extremely uncomfortable with your chest and try to hide it as often as you can (e.g. wearing hoodies) and would like to buy a binder to flatten it and make yourself more self confident. If she knows about trans stuff then i assume she'd know that trans people assigned female at birth would compress their chest. If you don't want to ask her then write a letter or a text? That's easier than face to face. Do you have your own debit card? I saved up for my first binder and bought it myself to save the awkwardness before I came out. Granted I was a couple years older than you are so it may have been a bit easier.
There are sometimes places that offer free binders for those that can't afford them. You could try searching this online. I can't remember specifically where. But I also know that the LGBT outreach near me, we'll in my province, sometimes does this too. They may not be the type or style you like but might be an OK starter one. Also, I don't know what size you (bra) are or whether you are actually out to her, but you could mention how you dislike your size and just wish you were smaller. "If I had to choose between big breasts or no breasts, I'd choose no breasts." Besides as honest as you feel comfortable with. It's normal for mom's to help daughter's with their first bra purchases, so saying you'd rather a binder instead of a bra doesn't have to be a weird thing. Just a variation on an already awkward right of passage.