I was once sending some local newspapers to someone. The seasoned postal clerk explained to me that Media Mail is only for books and DVDs. Magazines and newspapers were not included because Media Mail if for educational items only. Now maybe ads are the reason magazines and newspapers weren't included but it wasn't the reason he gave.
I search all of USPS website and the tyvek were only for priority not flat rate. there are padded flat rate envelopes but they are not tyvek.