Hi,
Yes, 1941 regulations show that both the HJ bugle and the DJ fanfare had a "regulation Hitler Youth instrument eagle" (
vorschriftsmäßiger Hitler-Jugend Instrumentenadler) attached to the upper side of the flare and this could logically be such an item. I haven't personally seen any period books that show the instrument eagle in detail but still, the type you show there is a worry. The eagle on bugles that are considered "good" have a scroll and are generally different to the one you have there.
Here is the eagle on a bugle that is considered to be authentic.
Here's another bugle with the same type of eagle and also with the regulation artillery red cord:
http://www.hj-research.com/forum/f38/hitler-youth-hj-bugle-rjf-eagle-7710/
Here is a fake from Pakistan and as you can see, it has your type of eagle on it:
http://www.hj-research.com/forum/f66/fake-hj-bugle-3729/
Here's another:
http://www.hj-research.com/forum/f38/hj-bugle-genuine-1700/
All of this is a strong indication of how the correct eagle
should look but we really need an illustration, photo or description of the regulation eagle from the period to move forward. Having said that, eagles of the type you show seem to be too "available" and this sets off alarm bells for me.