The problem is not 'burning' hydrogen. That's been done for ages. The problem with hydrogen powering aircraft is figuring out where to store the hydrogen. Hydrogen has an incredibly low energy density by volume. Because of this (and other) basic physics problem(s), hydrogen will not work to power planes on long duration flights. The most likely solution to decarbonizing intercontinental aircraft travel will be some form of liquid bio-fuel or even synthetic liquid fuel.

Because of the expense of hydrogen, medium and short haul flights will most efficiently be covered by some combination of an expansion of high speed rail and battery electric aircraft.