If a dead body is being transported in the cargo section of an airplane, is it permissible for Kohanim to take that flight? The Halachic status of Tum’a rises from a human corpse, and we might therefore conclude that the Tum’a rises from the body in the cargo section to the passenger cabin above. If so, then it would appear that Kohanim may not fly on such a flight.
Rav Moshe Feinstein (Russia-Israel, 1895-1986), in his work Iggerot Moshe (Y.D. 164), indeed rules that it is forbidden for a Kohen to travel on an airplane that is transporting a human corpse. In his view, the presence of a body in the cargo section brings Tum’a to the entire airplane, rendering it forbidden for a Kohen to board the aircraft. Therefore, according to Rav Moshe Feinstein, a Kohen must verify before taking a flight that there are no bodies being transported on that flight. El-Al, which often transports bodies to Israel on its passenger planes, has an arrangement whereby certain flights are designated to accommodate Kohanim who follow this ruling, and the airline ensures not to transport bodies on those flights.
According to some authorities, this ruling applies even in a situation of a Kohen who is accompanying the body of an immediate family member, such as if a Kohen is flying to Israel with his deceased father to bury him in Israel. Halacha allows a Kohen to become Tameh for the burial of an immediate family member; he may attend the funeral and burial of an immediate family member, even though he will then become Tameh. However, some authorities maintain that this would not apply to flying on the same airplane as the dead body. They argue that this is not necessary for the burial, as the Kohen could travel on a different flight, and therefore, if we assume that the entire aircraft is considered Tameh, then a Kohen may not fly even to accompany an immediate family member for burial.
However, Hacham Ovadia Yosef, in his recently published work on Abelut, disagrees. He writes that traveling with a deceased family member for burial indeed constitutes "Sorcheh Ha’met" (serving the needs of the deceased). Since the Kohen travels to accompany the body and to make the necessary arrangements, the flight is no different from the funeral and burial, and it is therefore permissible. Certainly, then, a Kohen may fly on a flight to accompany the body an immediate family member for burial.
It must also be noted that Rav Shlomo Amar Shelit"a, Sephardic Chief Rabbi of the State of Israel, in his work Shema Shelomo (Y.D. 18), disputes the aforementioned ruling of Rav Moshe Feinstein and allows Kohanim to travel on airplanes that are transporting a dead body. He contends that the cargo and passenger cabin should be viewed as two separate compartments, since there is no access to one through the other. A person cannot access the cargo section from the cabin, and therefore the two should be seen as distinct domains. As such, the presence of a body in the cargo section does not bring Tum’a to the cabin, and it is thus entirely permissible for a Kohen to take a flight that is transporting a body in the cargo section.
As for the final Halacha, Kohanim who are lenient and fly on airplanes in which a body is being transported certainly have a Halachic basis on which to rely, in light of the ruling of the Chief Rabbi. At the same time, however, regarding those who are stringent we say "Tabo Alehem Beracha" ("they shall be blessed"), and a Kohen who has a choice of flights should choose the flight that is not carrying a body. As mentioned, if a Kohen takes a flight to accompany a deceased family member, then there is no concern whatsoever of a possible Halachic violation.
Summary: If possible, a Kohen should avoid flying on an airplane that is transporting a dead body in its cargo section, but those who are lenient in this regard have a Halachic basis on which to rely. In the case of a Kohen who travels with the body of a deceased family member for burial, then he may certainly fly on the same flight without concern.