The rich will support the burden of climate adaptation because the income from the tax can be used directly to help mitigate climate change.
The vast majority of flights are taken by a small minority of people; they're taken by the richest. Take the United Kingdom as an example: 70% of all flights were taken by 15% of people [0]. It certainly isn't the poorest taking these flights.
So taxing flights will have less direct impact on the poorest than one might think.
Having said that, I think a charge on carbon is more fair than taxing flights directly.
The vast majority of flights are taken by a small minority of people; they're taken by the richest. Take the United Kingdom as an example: 70% of all flights were taken by 15% of people [0]. It certainly isn't the poorest taking these flights.
So taxing flights will have less direct impact on the poorest than one might think.
Having said that, I think a charge on carbon is more fair than taxing flights directly.
[0]: https://fullfact.org/economy/do-15-people-take-70-flights/