The armband is from one of the Fliegertechnischen Vorschulen (Aeronautical Prepatory Technical Schools). I have seen a similar lot (the same?) offered at a German auctionsite for 200 or 250 Euro. If original, this price is OK.
The students at these schools were organized by HJ and the armband was worn on the lower left sleeve of the uniform tunic. It was later replaced by a rhomboid badge, also worn on the lower left sleeve.