Is it permisable for a kohen to fly on a plane with a dead person in the storage compartment?
This should be avoided if at all possible.
If it cannot be avoided it is permitted to fly.
There are a number of considerations that can be taken into account as possible reasons for leniency.
One is the general issue of an ohel zaruk (a moving ohel), whose status is disputed, and which many consider only rabbinic even if it is considered an ohel.
Another is the separating wall between the two floors, which can serve as a chatzitzah.
Another consideration is the opinion of the Raavad who maintains that Kohanim who are anyway tamei are not prohibited from entering an ohel ha-mes (though the Chasam Sofer writes that there is still a rabbinic prohibition; Rabbi Akiva Eiger 18 disputes this). A number of authorities side with the Raavad, though his opinion is not the basic halachic ruling, and cannot be relied on independent of other factors.
This is only a very brief summary, and there is much to write on this subject.
All in all, there is therefore some room for leniency, but only in an hour of need. Wherever possible, the circumstance should be avoided.