I think it most unlikely that there was a 'flying machine' aboard Titanic when she went down.
However, the manifest does quite clearly indicate 'machinery' and 'printed matter', as Dave points out.
Now, from here on...I'm just guessing ...OK?
1910-1912, quite a few years since the Wright Brothers triumph, and the Europeans are starting to catch up with the U.S. in aviation "big time"!
One of the reasons was their development of efficient, lightweight radial and rotary engines.
I've got fifty bucks (Canadian!) that says the Aero Club shipment was possibly a Gnome rotary, or Anzani radial, aero engine - with the appropriate workshop manuals etc. etc.
It could also have been, of course, machine tools and/or dies to produce the same in the U.S.
Anybody else got anything?
I've started trying to trace this interesting little 'sidebar' - but to date with no success.
I promise to keep in touch.
John M