Never heard the term flyaway "tube". A flyaway kit is generally a supply of parts, expendables, and or tools that are flown with the aircraft to facilitate mtc. in the event of trouble at a place where these items would otherwise be unavailable.
For instance
DL aircraft 6901-6904 are 757s that Dl acquired from ATA and are the only
AC in the
DL 757 fleet with steel brakes. The main wheel assemblies are different from the rest and are not stocked at many
DL line stations. So two main wheel assemblies are kept on board the
AC in the forward bag bin.
These flyaway kits are sometimes kept in boxes or containers so it's possible some airlines use a tube for flyaway kit stowage hence the term flyaway tube.
Not all
AC have flyaway kits and the contents of the kits depend on the need that is being anticipated.
Dl757md