>>3274I suppose it depends on what kind of insert is in there; plastic and cardboard are the most likely as far as I know, but I don't dissect a lot of hats.
If it has a cardboard insert, you could soak it in water, then hold it in the shape you want and let it dry. It'll probably hold the shape. I know this from accidentally washing hats with a cardboard brim insert and getting a totally wonky brim when it was done.
If it has a plastic insert, I don't know what the best way to proceed is. I'd imagine that heat would do the trick; you'd just have to be careful not to apply too much, as it might mess up the hat in some way. Too little though, and it might just spring back into the previous shape.
Personally, I like the flat-brim look, but it certainly does have cultural associations which I wouldn't blame you for wanting to escape. However, there are other ways to subvert the swagfag stereotype, such as wearing clothes with no obvious branding, wearing less ostentatious shoes, sporting a higher waistline, wearing more closely fitted shirts and pants, etc. But it's all up to you.