Who said flying on Shabbos is a problem? If you're taking off on Sunday and landing after Shabbos being that you're above 10 tfachim throughout Shabbos, you were never koina a shvisa so there shouldn't be any tchum issue. Furthermore the plane is owned and operated by goyim and I doubt rov of the flight are yidden, so that would make it muttar to be on board on Shabbos.